Since you are in lifting mode you need to transition to a running mode. This is what I did 2 years ago when i was more lifting than running
LIFT on normal intervals for a few weeks. Instead of doing heavy weights, drop you weight you are lifting to 50% of max and do 5 sets of 10 (i did squats and calf raises) Instead of explaining it, ill give my avg workout i did while i transitioned
1. stretch REALLY WELL
2. first set at 50% squats. Every time i came up i did a powerful/fast calf raise that caused me to nearly hop. Weight was about 200. My max was only 300, but i could rep 300 several times and never go higher. Really, use a weight you are comfy with and can rep many times
3. Go do an set of crunches or something. SOMETHING to do with Abs. Follow these abs by either some pullups or pushups (a rep set, wide, narrow, or normal spread)
4. STRETCH AGAIN. LEGS, ABS, and ARMS
5. Start over. If you know need more weight to challenge yourself, add 5 - 10 lbs. When you get to abs, keep it consistent whether it be burnouts each time, set # of sets, or set time. For arms, I would switch between pushups and pullups, changing grip (pullups) and arm width each time.
6. After the weight room workout I would go out and just jog a comfy pace for as long as i could. Usually about 1/2 a mile in the start and eventually getting up to 1.5-2 miles.
When I got up to the 1.5-2 miles comfy pace i figured i could intensify running and reduce the weight room area. And then i would run first and then go in and do about 3 sets of 8 or so with similar ab and pullup rotations.
hope it helps. I only did the intensive weight room for a couple weeks and then i was ready to run like a deer
STRETCH AFTER YOU RUN