The 18-year-old follows Paul George, who was sent on loan to Hamilton at the end of last week, and Tom Rogic, who has moved back to Australia to get game time with Melbourne Victory.
Another Aussie Bhoy, Irvine Jackson, has been at Kilmarnock since August, and the midfielder will remain at Rugby Park for the rest of the campaign.
Darren McGregor is to have his loan deal with Notts County extended for a further five months after performing so well with the League One side that he has attracted interest from a host of clubs, including Wolves, who want to sign him on a permanent deal.
Lennon is not prepared to sanction the sale of McGregor because he is very happy with the progress the 20-year-old attacking midfielder is making at Meadow Lane, and plans to bring him back to Parkhead in the summer to gauge how close he is to being added to the Hoops first-team squad.
Celtic are considering requests to take other young players on loan before the window closes next week, with Lennon convinced, if the circumstances are right, the experience gained is hugely beneficial.
Findlay has jumped at the chance to follow this pathway, and tweeted: Delighted to have joined @Morton-FC on loan till the end of the season. Thanks for all the messages.
The Cappielow side's new boss, Kenny Shiels, is using this window to revamp his squad.
Morton have released their two Slovakian defenders, Michal Habai and Tomas Peciar. The pair have now been deemed surplus to requirements.
Another former Celtic player, Derek Riordan, has been offered training facilities at Cappielow.