.....dual registration terms with Vanarama National League North side FC United.
The 19-year-old was a key player as Bolton Wanderers` under-23's won their division last season but left at the end of his first professional year to join FC United.
A left-footer who can play at left-back or in midfield, Lonsdale's last game for the Red Rebels was in the 2-1 away win against Kidderminster in October.
City manager Mark Fell told his club`s website: "Cole is an excellent player, he's got great ability, is physically well suited to the league and he's got a really professional mentality. He'll fit in well with the group and gives us some left footed balance which we've been missing."
Lonsdale is expected to make his Dolly Blues debut at the weekend in the Buildbase FA Trophy at home to Ossett United.