As someone who also attempts to balance weightlifting with running, I'm just gonna say straight up it's a bitch.
But, personal advice, running a full half is a lot different than running a 3, 4, or even 5 mile race. Something to keep in mind is terrain- it's easy to jog a hill when you're fresh. It's much harder after 10 miles of road have gone under you. I'd certainly advise replacing or supplementing some of the shorter runs with hill sprints, as:
A) Pretty much everyone can support hill sprints, as they are obscenely difficult, and,
B) It's an excellent way of increasing, but also importantly measuring the increase of, your work capacity.
I'd definitely advise running a half at least once before you actually race, simply because if it's been a while you need to get pacing back into your mind.
Finally, as I'm sure you're aware, it's incredibly easy to get injured running. Which will then fuck up your weightlifting, and then your life. So foam rolling, fish oil, and a cheap pair of shoes should go a long way in preserving your legs for both activities.
Good luck! There's no reason you won't be able to crush it on your timetable.