I’m currently struggling with this, I have such eagerness for lifting and a need to run that when I combine them, one always gets shafted. So far, putting my priorities first has always prevailed. I am in marathon training, so when I put my running before lifting (as a priority and as a workout-scheduling tactic) then my running benefits. Putting them both together has been positive for my running (extraneous lifting = stronger core = better running) but the extra effort of lifting has dragged down my weekly mileage from mid 50s to mid 40s.
What I’ve heard that others do (that has worked for them) is to bulk up before marathon training, with lifting in the “off season” (typically winter if you’re not looking for a Boston Qualifier time) to build muscle that will help your running, but eventually get “eaten away” by high mileage and a lesser lifting load. For some people this is frustrating because it feels like you’re gaining to then let it waste away, but the muscle you build initially will give you the endurance to distance run. What I’ve personally learned from trying to increase lifting gains and mileage at the same time is: A) don’t max out your lifts before any sort of important run like a long run, tempo or speed effort. B) lifting 3x/weekly is fine, but your gains will be very slow in both concentrations. Lifting 4x will be good for lifting and not running, while lifting 2x will be better for those focusing on running or during a taper period. C) Put whatever is more important first. Lift first in the day if you want gains there. Run first if you want to not feel like crap trying to slog through an 8 miler after you’ve deadlifted your bodyweight (ouch).
The plan I’m currently working on is lifting 3 times a week, on my days off from running as well as paired with “mileage-boosting” easy runs that are meant to put more miles onto my legs than be an “important” run (as I defined before). For me it’s more of a scheduling battle than anything, keeping my lifting away from my long runs and after the daily run. Best of luck to you!