100% I agree with Elastigirl that one of the first things I'd take a look at would be diet; specifically carbs vs fats vs fasting before bed. You may need to experiment a bit with it. Could also try to eat a slower digesting protein (casein is a common recommendation) prior to sleep. And AFAIK melatonin is typically most useful to 'reset' sleeping schedules, rather than encourage sleep quality long-term.
How close to bedtime are you working out? Does the sleep interruption occur if/when you change the time you do the activity? Personally I can't work out within about 5hrs of bedtime if I want to get anything resembling quality sleep. You could also try just going to bed earlier, which may disrupt the pattern enough to switch things up.
How are your overall stress levels? Gratitude journaling, meditation, yoga, and walking outside for a bit every day can help w/ elevated cortisol. If you wanted to explore supplement options, rhodiola and l-theanine are typically relatively safe to experiment with. L-glutamine is another one, but it depends on the person where it may either improve sleep or keep you up.
Have you had your thyroid levels tested? There are all sorts of connections between thyroid & adrenal glands/hormonal interactions. Also just blood tests in general, to rule out any nutritional deficiencies.
If it's really specific to lifting weights though, I'd experiment with staying hydrated and eating a larger protein meal asap after the workout. It may also be that your body temperature is higher on days that you lift, so you need lighter blankets on those nights and/or deliberately cool down your body prior to sleep.
Bodies are weird and wonderful things - and unfortunately complex when it comes to troubleshooting. 'Hope some of these suggestions may help!