No such hotel exists.

If you need a hotel from which you can transit to both airports inexpensively, I'd probably look for something near the transit plaza in downtown Long Beach, like the Westin, Renaissance Long Beach or Best Western Plus Long Beach Convention Center. Long Beach Transit bus 111 runs from the transit plaza to LGB. Meanwhile, you can use the Metro Blue Line train from the transit plaza. The Blue Line will connect with the Metro Green Line, and you can take the Green Line to the Aviation Blvd. station. At the Aviation Blvd. station, there's a free shuttle bus to the LAX terminals.

www.metro.net for info on the blue and green lines. www.lbtransit.com for info on bus 111.

So this wouldn't exactly give you door to door service, but it would allow you to reach either airport for only a few dollars each way, per person.