Thank you Frances,
The confirmation that there is a son William comes from Edmund's administration in 1803 which is transcribed on BL's site
The unborn child is my wifes grtx3 Grandfather who Mary names Edmund.
The pledges are interesting - Edmund's brother William Garrett and Nicholas Cowley (who is almost certainly Mary's brother in law)
Whilst the Lezayre connection is likely as you suggest from a research perspective this is very much a German family seemingly based around the Greeba area.
One possible line we have tried is that the William named in Edmund,s administration as his brother, is in fact the William Garrett who marries Jane Kissack in 1822 in Braddan, and dies in 1840, being buried in Lezayre. There are two interesting co-incidences - William is a shoemaker and so is Edmund & William names one of his sons Edmund. Apart from those coincidences we can find no real evidence.
Mike