Should I cite a result if the paper doesn't include a proof?
Citing the other paper seems necessary in any case, as they have stated the lemma before you. This is for attribution. Citing the other paper for evidence seems not appropriate, as there is no proof given there.

If the lemma is not rather obvious (say the obvious proof strategy works in &lt; 5min), then stating it without proof would be very bad form. Put in an appendix if you don't want a boring lengthy proof to spoil the otherwise elegant paper, but put it somewhere people can find it.