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I searched on the subscription site Roots Ireland and did not find any baptismal records for children of Lawrence Corcoran and Bridget McDonald. Many of the RC parishes in Co. Leitrim have records starting later than 1840. I also checked the 1857 Griffiths Valuation head of household listing for Co. Leitrim and although there were five Corcoran records none were Lawrence.
You may want to add Michael Corcoran to our XO Chronicles site. https://irelandxo.com/ireland-xo/history-and-genealogy/ancestor-database