I searched the Irish Family History Foundation's database for Louth. Rcds B4 1840 are sparse.
For Joseph Leech (+variants) B abt 1800, I found 0 B rcds, then, or ever.
For Joseph Leech (+variants) M abt 1820, I found 1 M rcd in 1822. For Mary Tracy M abt 1820, I found 0 matching M rcds. This implies the event wasn't rcd'd, rcds didn't survive, occurred elsewhere, or hasn't been digitized. However, I have found 2 instances where only 1 rcd for either the bride or the groom was rcd'd without a rcd for the other party.
For Thomas Leech, B 1824 in Termonfeckin, there is 1 B rcd. A view of the detailed rcd may reveal info abt the parents, addresses, occupations, etc.
Google the Foundation's name to lead you to the database. Post a follow-on msg to Genforum to tell me your search results.