Don't know what you routine is like, but I found last year once a week was enough to add significant distance, I was sprinting every week anyway, and added in a longer run, separated as much as possible in my routine. I was able to add a mile most weeks, and was up to 10 miles in a couple of months easily.
I could have added distance quicker but at the start of was building up speed too so wans't adding miles untill I was doing a 10 min mile at the previous distance. Then as the race I wanted to enter got closer I decided to run the distance and work on getting faster each week.
I do not have the build of a runner either, so it's not something I'm naturally gifted at.
So if you have a spare day or a light day you could do it without dropping any of the lifting, and at worst you'd have to drop a day and go easy on the legs the day after. Of course YMMV this is what worked for me and what I'll do to train for a marathon.
You know all those pictures of Adam and Eve where they have belly button? Think about it..................... take as long as you need........................