Upvote:0
I don't think you should. You live in the US, not just visiting.
Upvote:1
If you are in doubt about including something on a visa application, include it. The UK and the US share immigration data, and UKVI will know about your US entries. If you don't mention them, UKVI may think you're not being honest.
You should also mention in the application that you currently live in the US on an L-1 work visa. This supports your application by showing a good reason for you to leave the UK after touring the UK.