Either do a little less (few sets less, or cut an exercise) in your workouts, or you could switch to a fullbody split where you're doing only one exercise for each area in any given session. At least untill you build up a tolerance for weight training.
The other option is to pre-exhaust the lats by isolating them before doing your main exercise. E.g. Straight arm pulldowns before pullups, pullovers before rows etc etc.
Personally, if you're new to training i would go with the fullbody split option.