The midfielder is out of contract in the summer and has not yet accepted an offer to remain at McDiarmid Park.
The 24-year-old says he is in talks with other clubs and has yet to make a decision on where he will be playing his football next term.
Davidson impressed during Monday's 3-1 win over Hibernian and, for now, Lomas is willing to settle for more of the same.
"It's down to Murray, its up to him what he does," said Lomas. "If you looked at the level of his performance against Hibs, as long as he keeps playing like that we will be delighted. We would like to keep him but that's Murrays prerogative.
"We're happy he's back from injury. He played fantastically well the other night and we hope he keeps it up until the end of the season."
Davidson has been targeted by Rangers in the past and was again linked with the Glasgow giants in December.
The Ibrox club are under a transfer embargo but can secure players on pre-contract agreements before registering free agents on September 1.
However, Lomas has refused to be concerned about a possible swoop by the Irn-Bru Third Division leaders.
He added: "It's not a worry because you can't do anything about it. There is no point worrying about something you've got no control over.
"Our focus is on trying to finish as high as we can this year."