You would need to check the insurance situation with the bike's owner, but when we borrowed a bike from a friend in 2004, his insurance covered us. He did, however, take the precaution of issuing a simple letter of authorisation, just in case we ever got pulled over. (We didn't.
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More tricky is likely to be the reverse situation, if you have offered a reciprocal bike loan in the UK/Ireland. Having been loaned a bike in the US, we naturally offered to loan one of ours when our friend visited the UK. Our insurers didn't want to know and put up all sorts of ridiculous conditions - despite American driving licenses being recognised as perfectly valid for car hire etc. I don't know whether Irish insurers are a bit more amenable ...?
As to what to see in August in LA ... I would advise you to get as far away from LA as you can. The heat and smog would be unbearable. Personally, I would head north. The Pacific Coast Highway is iconic, but slightly spoiled by queues of motorhomes. In 2009, we took the inland Hwy 33 out of LA instead and, once we had left the weekend traffic behind, we had a beautiful couple of days riding through the wine growing areas and into San Francisco via Alice's Restaurant and the Skyline Boulevard. From San Francisco, I probably head inland to Yosemite National Park ... You could then head East via the Extraterrestrial Hwy (Hwy 375 - so called because it borders Area 51). Stop for an iced tea in the Little A'Le'Inn café at Rachel, Nevada (Very weird. Attracts a lot of UFO fanatics - like something from a Larson cartoon.) From there head into Utah. May be stay in Kanab and visit Monument Valley and the North Rim of the Grand Canyon. Go back to LA via Las Vegas ... Actually, with three weeks, there's masses to see and everyone will have their own favourites.
Have fun.
