Some further notes...
While LGA can be a bit rough and ready, I've always found the UA staff on the premium check-in desks to be excellent. Faced with a LGA-IAD delay of more than one hour, they once paid for a cab to take me across to JFK where there was an on-time flight available in order to give me a better chance of making my IAD-LHR connection. I've also found the RCC staff at LGA quite helpful.
IAD is a different matter

But the connection in your case is straightfoward. I've done it in under 5 minutes.