The Scottish left-back has yet to make a first-team appearance for Premier League outfit Cardiff this season but is wanted by Weir for his experience.
"We are hoping to get it done by tomorrow but he has not got the clearance yet [from the Welsh FA]," he told reporters. "As long as he does not get the clearance, he won't play. We hope to get him and once we get him, it would be good to get him involved.
"He is an experienced player. He has been here with us for a couple of days and is that kind of character who is full of life, and that is going to add to our group. We will try to sign him as soon as possible.
"There are clearance issues with the Welsh FA. I hope to play him tomorrow night [against Crawley Town] but I am not 100% confident."
Lappin has played for St Mirren, Norwich City, Motherwell and Cardiff in his career.