I've recently started running again, after a number of years.
Whilst I'm physically in reasonable condition from all the cycling I do, every run I've gone on since I started again, I encounter this same problem after about 10 mins – I get what feels like a lactic acid build up in my shins, which is very painful, and I have to stop and stretch off, after a couple of mins I'm good to go for an hour or more, no more lactic acid.

Has anyone any experience of this?
Will it stop?

Or do I just need to MTFU?

pretty unlikely to be lactic acid

Shins splints?

Are you running heavily on your heels? Over-striding can also cause them, and I've heard people saying it's common with cyclists because of over developed calf muscles.

Goes away normally, or if problem persists think about getting your stride anaylised at a running shop