The Lexus Part Number is : 12361 20060. Aftermarket part number which I swear I will not be buying is 4202.

There is a similar looking part that fits the 2000 to 2004 Avalon. The Toyota Part number is 12361-0A050 and much cheaper than Lexus part.

Question is - are they interchangeable?

 

I just installed an OEM Lexus 1236120060 front mount, and the other three in Lexus.
Ebay $179.
1mz engines chatter at idle. I've read that aftermarket mount are so poor that tbey've been removed from tbe market.
I got the OEM Lexus front shock from UAE. Good price and it arrived within a week.
The 20060 mount is vacuum modulated for quiet idle.
Various Lexus and Toyota dealers offer deals online. Hendricks and Bells supplied mine.
If all things, motor mounts and seals are best as OEM.
An AWD RX has considerable weight stuck on the backside of the engine that an Avalon doesn't have. It might work as in "fit the holes" but it also could induce cabin noise and harmonics into the body.
UFm
If rhd part numvers are different, something's different.
Unless collapsed, I'd leave the old mount in before going with aftermarket. Especially the rear mount. The front us easy to replace. The rear is not.
the rear pic us sans steering rack and sway bar.

 

Unsure what ails your existing front motor mount, but I've removed a '20060 220k mile OEM mount that was not causing problems.
I you want the mount, it's yours. If near south central NC, pick it up.
I have all the old motor and trans mounts. None in failure condition. All soon to be trashed.
Also have an AC compressor with a good clutch. Smooth bearing. The compressor was working without issue, but has been operated for several years without adequate lubricant. Found that when doing a transmission and general freshening. Also heading to the dumpster unless someone wants it?