The short answer is no. (But please read all the way to the bottom here, because you have a new option...)
*As a Southern Californian, I can tell you that you will not find a motel between Ludlow and Needles along the old Route 66 corridor. The historic motel in Amboy (Roy's Motel & Cafe) awaits restoration. (rt66roys.com)
*If you're curious about going Victorville - Apple Valley - Lucerne Valley - Landers - Yucca Valley - 29 Palms - Earp/Parker (basically following CA 18, CA 247 and CA 62), you have reliable motel choices in Victorville, Apple Valley, Yucca Valley, Joshua Tree, 29 Palms and Earp/Parker. Lucerne Valley has one motel, and I haven't laid eyes on it in person. Landers does not have a motel at present, but it does have some interesting Airbnb rentals and Kate's Lazy Desert, a glamping resort owned by Kate Pierson of the B-52s (lazymeadow.com/lazy-desert.html). Your big problem is the totally motel-free stretch between 29 Palms and Earp/Parker.
*Some road notes if you are considering the route described in the paragraph just above:
1) Victorville and Apple Valley have some bike lanes (more of them in Apple Valley than Victorville). Check Google Maps and see if any of them parallel CA HWY 18, because
2) CA HWY 18 is not much fun for cyclists through those two cities.
3) Going this route, you would leave CA 18 in "downtown" Lucerne Valley and take CA 247 toward Landers and Yucca Valley. CA 247 (Old Woman Springs Road) is shoulderless (and many people would say dangerous) for the 20-odd miles between Lucerne Valley and Landers. It does now have an excellent shoulder (4-6' wide) from the middle of Landers south into Yucca Valley, though blowing sand can drift onto the southbound shoulder (you can see some of this, in fact, on Google Maps satellite view).
4) CA 62 has a very dangerous, shoulderless stretch between Joshua Tree and 29 Palms (high-speed traffic, and it's an east-west road which means blinding sun for drivers at sunrise/sunset). That is why many touring cyclists opt for going through Joshua Tree National Park instead (tough climbs, but less dangerous roads; brings you back to CA 62 at 29 Palms).
5) East of 29 Palms, CA 62 is much less trafficked. Much, much, much, less. It feels more like a rural highway in Southern Arizona. But there is nothing - as in no services, absolutely nothing - until you get to tiny Vidal Junction, which has a gas station/convenience store. There's also a big CA agricultural checkpoint there. People do camp along CA 62 between 29 Palms and Vidal Junction, you see some RV "boondocking" on some of the hardpan along the many miles between those spots.
*It is May. Are you thinking about crossing the Mojave in spring or summer on a bike? Don't. DON'T. Mojave Desert heat is frighteningly dehydrating. May 4, it is forecast to hit 98 degrees in Barstow. Cools back down to 73 degrees on May 7, but the point is that the hot weather is now here.
*NEWS FLASH...
*There is a NEW OPTION for getting across the Mojave Desert that most touring cyclists have not heard of. Yet.
vvta.org/bus/route-200/
Last year, Victor Valley Transit introduced Route 200 - the Needles Link.
I just called VVTA, because I'm curious about it myself. The operator said the bus has a standard bike rack up front (fits 2 bikes).
$12 to get from Victorville to Needles (or vice versa), with a stop in Barstow in between. $6 if you are a veteran or a senior.
Downside - it only runs on Fridays. And you need to make reservations (see link).
But ... if you find yourself in Needles or Barstow or Victorville on a Thursday with the perilous crossing of the Mojave ahead of you ...
You might think about arranging your tour to sync with catching Route 200 across the Mojave.
Another way to bypass the long, warm, motel-less stretch of the Mojave is to take Greyhound or AMTRAK from Victorville or Barstow to Needles ... but they aren't really bike-convenient options. Both options mean traveling without your bike and meeting it down the line. The AMTRAK stations in Victorville, Barstow and Needles don't have baggage services, so you'd have to ship your bike along that way by other means. Shipping your bike from Point A to Point B via Greyhound? Not recommended.
