The name Leece (and Lace from which it probably derives) seems to have provoked much dissent between the main writers - J J Kneen (see www.manxnotebook.com/fulltext/pn1937/intro.htm)) writes:
The names Leece and Lace are like the unfortunate pebble to which I have just referred, for they are worn so much that there is nothing but the core left. Leece began its career in the grandiloquent form Mac Guilley Yeesey, i.e. 'the son of Guilley Yeesey', a personal name meaning 'the servant of Jesus', a post-Christian name. The name Lace may belong to preChristian times. Its oldest form was Mac Guilley Chass, i.e. 'the son of Guilley Cass', which latter means simply 'the curlyhaired youth'.

A W Moore in his 1880's book tentatively suggests a Scandinavian origin possibly from Leif, or Leifr, 'an inheritance,' (see www.manxnotebook.com/manxnb/v10p053.htm)

However W W Gill pointing out the lack of any surviving 'Mac' prefixed name in the Manx records suggests a possible English origin (see www.manxnotebook.com/fulltext/scrap3/ch01.htm)

So you are free to make your own choice !