since tempos are used for recovery would it be ok to do them right after a lower body weight training session?
You could do this but what did you do the day before and what will you do the day after? If it was another high intensity day then thats 2 high intensity days in a row. You want to try and segment your training so you do high intensity, low intensity, high intensity. Leg work will be high intensity (assuming you are doing a fair bit of weight).
We did tempo after leg weights last year in-season (with success). I’d have them lift as early in the day as possible then we’d run tempo at team practice in the late afternoon. The day after was also low intensity tempo.
Ideally, you probably don’t want to do tempo after leg weights (especially immediately after) but I know your schedule sometimes may not allow it.