For Alexander Jnr, there is a possible marriage in 1888, 2nd Qrt West Derby, vol. 8b/pg. 319:
Alexander Gibson and, on the page, a Helena Fitzsimmons.
I thought this might be them in 1891 in West Derby:
Alexander Gibson 26 sheet metal worker b. Scotland
Helena Gibson 20 b. Ormskirk, Lancashire
John W Gibson 2 b. Ormskirk, Lancashire
Lydia A Gibson 1 b. Ormskirk, Lancashire
I think Alexander Jnr may have died between censuses. By 1901, Helena looks to have remarried to a William Lee. The family in Ormskirk for that year:
William Lee 33
Helena A Lee 30
Lydia A Gibson 11 Stepdaughter
Alexander Gibson 9 Stepson
James Lee 3
Helena Lee 1
John Lee 31 Brother
As a possibility, there is the death of a 27 yr old Alexander Gibson in the Lancashire Parish Registers for Ormskirk who was buried on 20 May 1893 (ref statutory registers 2nd Qrt 1893, vol 8b, pg 164).
Monica