Only 1 works. 2 is incomplete (with what?). #3 doesn't work with "for" (for me).
Which are correct:
1)That instrument was taken to the lab to repair the pipes.
2) That instrument was taken to the lab to repair the pipes with.
3) That instrument was taken to the lab for repairing the pipes.
I vote 'None of the Above'.
In none of your examples is it clear whether the pipes being repaired are part of "the instrument" or if the instrument was somehow used in the repair of pipes not a part of the instrument itself.
It's unusual to take something to a laboratory to do repair work. I certainly think of instruments being in a lab and being taken somewhere else to be repaired or perhaps needing to do repairs to something in a lab because it can't (or needn't) be removed, not the other way around as inferred by your examples.
Best guess is: There are pipes in the lab that need repair, and an instrument is needed as part of that repair. Your #2 comes pretty close to that. Better as: That instrument was taken to the lab for use in repairing the pipes.