This is years ago, but when I was doing strength workouts, I found that I was burning through my sugar reserves. It takes a while of running before your body moves from burning mostly sugar to burning an even mix of sugar and fat. It does it faster the more cardiovascularly fit you are, but when you first start it can take up to 30 minutes. If you only run 1 mile, you aren't getting there.
I recommend swapping the running and lifting for a couple of months until you get that working better. Once you are running 3-5 miles then you'll give yourself enough time to switch to burning fat as fuel and you won't have so much trouble running after lifting (the first mile is always hard, though).
Or at least that was my experience. Haven't done it in more than 20 years... (stopped lifting -- kept running ;-) ).
If you're doing lifts first, you're not giving your body a chance to adapt to the cardio. Maybe switch it up and one day a week run first then lift. Then maybe add a just running day.
I recommend swapping the running and lifting for a couple of months until you get that working better. Once you are running 3-5 miles then you'll give yourself enough time to switch to burning fat as fuel and you won't have so much trouble running after lifting (the first mile is always hard, though).
Or at least that was my experience. Haven't done it in more than 20 years... (stopped lifting -- kept running ;-) ).