The left-sided wing-back, who played from the start as the struggling League One side snapped a six-game losing streak in a 1-1 draw against Crawley Town last night, has arrived in Yorkshire after being omitted from City's 25-man Barclays Premier League squad.
The former Scotland Under-21 cap only joined the Welsh club on a permanent deal in January after initially going out on loan from Norwich City.
Lappin, who began his career at St Mirren, said: "I am really looking forward to the challenge and this is a great opportunity for me. I want to play some games and help the lads out of the current predicament we find ourselves in.
"When you aren't playing at your club, going out on loan is a fantastic option, but first and foremost I just want to contribute to helping the lads."