[A drawing is in the works--I'm late with this owing to my recent travels.]
A Lücke is a gap or narrow opening and a Büßer a penitent. However, the ~büßer part in Lückenbüßer derives from a now obsolete meaning of the verb büßen: To improve upon or correct something. So, a Lückenbüßer is someone who fills in for someone else without being really qualified for the job. The term is closely related to Notnagel, our word of the month for 9/2008, where the latter term is, possibly, a little less derogatory than our current word of the month.
Note that in spite of its outdated use of büßer, this compound noun is very much in use in present-day Germany.
3 hours ago