No need to use oil, especially with Latigo. The best conditioning is from the "palm rub" - before stropping run your palm across the leather about 50 laps or so. Not only does this warm up the leather but the natural oils from your hand will be transferred to the strop, which should be enough to keep the leather supple for quite some time.

About 60 laps on leather sounds right. I typically do more fabric laps than our friend thebigspendur, usually in the neighbourhood of 30-40. YMMV.