Can I split my HIIT and weightlifting sessions at the gym?
Absolutely. In fact, this is the optimal & ideal way to apportion your training activities.
How a particular training style or strategy will affect you depends on a number of variables, both extrinsic & intrinsic. For example:
Extrinsic variables will include: exercise duration, volume, time of day, intensity, weight lifted. It will also include diet, drugs and supplements used.
Intrinsic variables will be things like genetics, age, health status, etc.
True HIIT training is a short duration, high intensity, by definition and it’s very nature, a self-limiting activity. In other words, you can’t maintain it for long, if you’re doing it properly.
Weight training (not powerlifting, not Olympic Lifting, not cross-training) perhaps let’s call it bodybuilding here for precision, where the main goal is muscle hypertrophy, consists of a higher volume, more controlled & focused, less intense, longer duration activity.
Your body’s physiology will use both common (immune system mechanisms) and dissimilar (mTorgeneration vs ampk release). I’ll avoid getting overly technical about it and put a wrap on it by saying that the best result will come from you separating these activities as much as possible and allowing yourself to recover and essentially giving yourself time between them to reload.