Disregarding your age, and looking purely at lifting and running. It's not hindering your running, unless your recovery time is making you too sore that it eats into your running. Don't give up the squats, they're great for your quads and nothing builds your core better than squats and deadlifts (make sure you have proper form for both, and going parallel on your squats). I've been lucky enough to never have any problems with my lower back and core area while running for I focused on a 5x5 barbell strength programme before getting more into running. Resistance training should be part of your weekly routine.
I've personally given up most of the lifts, apart from squats for I was just getting too fatigued and my goals have changed as I've swtiched from strength to endurance (10-12 reps per set at a lower weight). Try looking into doing leg press as well as squats, and lunges are also good for your core/legs.
Just tailor your lifting more towards your running goals. For example, are you training for strength or endurance? Trying to build mass isn't going to help your running too much at all.
Edited: 25/07/2012 at 11:20