In a recent book, Guardian of the East India Company: The Life of Laurence Sulivan
By George K. McGilvary, the possible Cork origins of Laurence Sulivan are explored. Google Books provides an extract showing the various links.
http://books.google.ie/books?

In one of the books on Sullivan it is suggested that he was an illegitimate older brother to Benjamin Sullivan. It also suggests that his Christian name Laurence (Larry) is the English version of the Irish Leabhrás, a common name in the O’Sullivan Bere family.

Benjamin Sullivan (1720-76( was a State Attorney for Cork City and County in the early 18th century and he was described as a ‘Kinsman’ to them. His father was Philip and his mother was an Irwin described as a Presbyterian, he was born in the Parish of St. . Two of Benjamin’s sons went to India, his influence did them no harm (is fearr focal sa Chúirt ná punt sa sporrán!) did well and later became MPs in England.

Looking at deeds in which the Cork Sullivans were involved as attorneys on the Registry Of Deeds Project:

http://irishdeedsindex.net/deeds_index/name_index.php

quite a number eminate from the Mizen area.  In 1700 Bishop Dives Downes on his tour refers to landowners in Schull including Mr. Sullivan, a Protestant.

1720-1767 Benjamin Sullivan Attorney, Barrister, 1752 Clerk of the Crown for Counties Cork and Waterford. Thomas Harrison writing clerk to him 1742, Married Bridget Limerick daughter of Dr. Limerick, Rector Kilmoe (Ballydehob), 1742 Father Philip mother Elizabeth Irwin a Presbyterian, Parish of St Paul. Benjamin Sullivan Senior Esq., eminent Attorney died London 1767, May have been Recorder of Cork 1765. son Sir Benjamin Sullivan, Kt, Judge Supreme Court Madras, the Right Hon John Sullivan of Richings Park, Co. Bucks, Privy Councillor, MP Old Sarum, Sir Richard Joseph Sullivan Captain RN and MP for Seaford Baronet UK 1804. Protest against him being appointed Freeman as he allegedly did not serve 7 years as an apprentice, 1742, Memorial 77771. May be related to Laurence Sullivan speculation the Laurence was an illegitimate elder brother and so Lawrence may be variation of Lábhrás a name common among the O’Sullivan Beres, Chairman of East India Company. Parliamentary biography gives his address as Dromeragh. (Dromreagh Durrus?) http://corkgen.org/publicgenealogy/cork/potpourri/corkancestors.com/Deathsmarriages2.htm Oldest son Benamin, 2nd son John,Memorial 1764, 161080, Thomas Lyd Councellor mentioned with John Lloyd Victualler, Cork

https://docs.google.com/spreadsheet/ccc?key=0AqhnQGE3ANjzdEkxdVM0YVNzbzFHbV8tRGxNM2pmMWc&usp=drive_web#gid=0

id=x8St6IV3aOIC&pg=PA5&lpg=PA5&dq=laurence+sulivan+east+india+company&source=bl&ots=g3UStkvm_s&sig=ROeZVLd3_LUWnN6o6oYdIRhRsPk&hl=en&sa=X&ei=Z86wUqzINpSg7Abe1YGgAw&ved=0CDwQ6AEwBw#v=onepage&q=laurence%20sulivan%20east%20india%20company&f=false

For a brief outline of his Parliamentary career:
http://en.wikipedia.org/wiki/Laurence_Sulivan

Sullivan Lawyers Cork:

1708, 1709, 1715, 1728, 1783? same? John Sullivan 1709 Registrar. Attorney/Registrar, 1763 Comissioner. 1771 listed as Clerk of the Crown with Benjamin Sullivan for Co. Cork and Waterford.1771 Coroner Cork City. Ancient Freeman. 1710 Thomas Banfield a clerk later atorney. 1709 Named in Council minutes, in some deeds a John Sullivan Junior 1709 Commissioner for Affadavits, Memorial 1719 23650 Executor in will 1729 of Charles Newman Irish Manuscrit Commission 4
1756 John Sullivan Clerk to Benjamin Sullivan, Coroner 1767 May be John Sullivan Junior Attorney. Cork election Hely Hutchinson papers 1783, attorney Christ Church Lane. 1767 that £12 19s. 3d. be paid John Sullivan, gent., one of the Coroners, expense in feeing lawyers and prosecuting Robt. Murray for the murcdler J of Capt. Rea; http://www.corkpastandpresent.ie/history/caulfield_complete.pdf
1799 John Sullivan Master In Chancery Memorial 500 Other names John Austen, Thomas Austen, witnesses, John Bayly

1720-1751, 1746, 1749, 1767, dead 1767 Benjamin Sullivan, self styled O’Sullivan Mór, according to Denny Lane Attorney, Barrister, Notary Public, 752 Clerk of the Crown (State Solicitor) for Counties Cork and Waterford. Thomas Harrison writing clerk to him 1742, Married Bridget Limerick daughter of Dr. Limerick, Rector Kilmoe (Ballydehob), 1742. 1771 listed as Clerk of the Crown with John Sullivan for Co. Cork and Waterford. By an order of 26 April, 1749, Benj. Sullivan, Attorney ; Mr. Will. Snow, Attorney and Mr. Thos. Allyn, Attorney, be admitted free. I, Hugh Millerd, Jun., do protest to the makeing of Mr. Benj. Sullivan,
Mr. Wm. Snow, and Mr. Tho. Allcyn free as they diu not serve seven years’apprentiship, nor a sufficient Council at the time, the questions being put,only the unucrnameu: Mr. Mayor, two Sheriffs, Recorder; Alden. Atkins,Farren, Hulcatt, Owgan, W estrop, Wintrop, Travers.
Father Philip mother Elizabeth Irwin a Presbeterian, Parish of St Paul. Benjamin Sullivan Senior Esq., eminent Atttorney died London 1767, May have been Recorder of Cork 1765. son Sir Benjamin Sullivan, Kt, Judge Supreme Court Madras, the Right Hon John Sullivan of Richings Park, Co. Bucks, Privy Councillor, MP Old Sarum, Sir Richard Joseph Sullivan Captain RN and MP for Seaford Baronet UK 1804. Forbes, Gordon, Captain, 34th Regt, to Miss Peggy Sullivan, dau Benjamin, Esq., late of this City, at Christ Church – (HC 17/9/1770). 1746 WD WM SULLIVAN Denis of Shanagh, KER Farmer
E WD DUGAN Mallaky of Clarogh, COR Dairyman
F WM SULLIVAN Benjamin of Cork City Gent. Maziere Brady recounts Bishop Dive Downes tour of Schull/KIlmoe 1700 he notes land owners Limrick Mr. O’Sullivan, a Protestant.
p.172 http://www.corkpastandpresent.ie/history/batch2/bradyvol1/#/244/zoome
Protest against him being appointed Freeman as he allegedly did not serve 7 years as an apprentice, 1742, Memorial 77771. May be related to Laurence Sullivan speculation the Laurence was an illegetimate elder brother, d so Lawrence may be variation of Lábhrás a name common among tthe O’Sullivan Beres, Chairman of East India Company. Parlimentary biography gives his address as Dromeragh. (Dromreagh Durrus?). SULLIVAN, BENJAMIN – (5/11/1770) – To be let from the 25th of March next, several lots of ground in Fair-lane and Peacock lane in the North suburbs of this city. Proposals will be received for Benjamin Sullivan, Esq; by Mrs. Sullivan on the Mall. http://www2.ul.ie/pdf/943693677.pdf. 14 July 1747 Affidavit of serving order to pay the money levied
on the execution to the defendant John Armstrong sworn by Cornelius Sullivan in front of Benjamin
Sullivan.

6 June, 1767. That William Jones, gent., having served Anthony Lane, Esq. ; Benjamin
Sullivan, Esq., eldest son of Benjamin S., Esq., dec.; Be admitted freemen

http://corkgen.org/publicgenealogy/cork/potpourri/corkancestors.com/Deathsmarriages2.htm Forbes, Gordon, Captain, 34th Regt, to Miss Peggy Sullivan, dau Benjamin, Esq., late of this City, at Christ Church – (HC 17/9/1770). MARTIN, DANIEL, Wines & Porter, lived in Mallow Lane, now removed to the house wherein Ben. Sullivan Esq. Formerly lived at the corner of the Fishambles near the Exchange, (CJ 4/10/1756) ; 1767 Richard Martin, gent., having served Benj. Sullivan, Esq., and Mr. Wm. Snowe;
admitted freemen at large. Present–Mr. Mayor, Sher. French
Oldest son Benjamin, 2nd son John,Memorial 1764, 161080, Thomas Lloyd Councellor mentioned with John Lloyd Victualler, deed of 1750 mentioned wit George Dunscomb and Nicholas Weekes, Councillor Cork 145. 7 July 1767 Deed of assignment of judgement against Francis
Strange by Bridget and Benjamin Sullivan, Cork, (executors of will of Benjamin
Sullivan St. James Square, London), to Adam Newman, Cork, for £116-19s-2d.
Witnessed by Margaret Sullivan and Elizabeth Sullivan.
1735-, 1783 Sir Benjamin Sullivan Barrister 1770, Puisne Judge Supreme Court, Madras Eldest son of Benjamin, Clerk of the Crown for Co Cork , Recorder of Cork, Ó Sullivan Mór, Bridget Limrick Goleen.Cork election Hely Hutchinson papers 1783, listed as East Indies, item 626 Admission Middle Temple Register 1in 1764, 1661-1781, Vol 1, Linen Hall Library Belfast, 1735. Dublin Almanac 1798. As Benjamin Junior. Subscriber of 1766 ‘The History of the Irish Rebellon’, Cork, 1766 6 June, 1767. That William Jones, gent., having served Anthony Lane, Esq. ; Benjamin
Sullivan, Esq., eldest son of Benjamin S., Esq., dec.; Be admitted freemen