Lamm phono stage LP2.1 Deluxe with low output ZYX MC cart

For most MC cartridges, as Chakster said, any load resistance above 100 ohms will certainly "work".  People do argue about how a particular load resistance "sounds" with a particular LOMC cartridge.  If you will read the contentious thread on this subject that is still alive, you will see that most agree the load should not appreciably affect frequency response, until you get way down near the internal resistance of the cartridge itself.  You won't have that problem.  I suggest you can ignore the issue; you cannot do anything about it anyway, as your Lamm seems to use a built-in SUT to derive gain sufficient for your cartridge.  It also seems the secondaries of your built-in SUT are loaded with the 47K ohm resistor used when you connect an MM cartridge.  I am guessing that the SUT has a 1:10 turns ratio, which means it increases the output voltage of the cartridge by 10-fold, to drive that 47K resistance.  (10-fold voltage gain is the same as "20db" of gain, quoted by someone else.) Since the net resistance "seen" by the cartridge is fixed to the value obtained when 47K is divided by the square of the turns ratio (in this case, 10^2 = 100), your MC will see ~470 ohms (47K divided by 100).  You cannot change this without some surgery to your unit, and I don't recommend it. You'll be fine.

What load do you think is best?

It is interesting question.
If your phono stage has a built-in (1:10) SUT then i can tell you that i have similar phono stage from another manufacturer and it was OK with ZYX LOMC cartridges.

But the ZYX CPP-1 pre-preamp i have mentioned was better and much more impressive for the sound of my ex ZYX cartridges. ZYX CPP-1 Headamp is active device (battery powered) and connected to MM phono input.

With different MC phono stages (with optional loading like my modified JLTi or stock Gold Note PH-10) i never use 100 Ohm with MC cartridges, mostly 500, 1000 or 10 000 Ohm.

However this is personal preferences and system dependent.

I’m the last person to notice microscopic changes in sound due to tweaks, etc but I’m somewhat surprised people can’t hear the differences in various MC loading.

Who said "people" can't hear differences due to loading an MC cartridge?  Speaking for myself, I simply advised the OP that the fixed loading afforded by his particular phono stage would be fine.  He has no other choice without spending many $$$.  Also speaking for myself, I have been using 47K with two of my LOMC cartridges (ZYX Universe and Koetsu Urushi), but two of my phono stages do not easily permit it.  (I have 3 phono stages in rotation using two entirely different systems.) In my additional experience, loads down to about 1000 ohms for those two LOMCs seemed a bit superior to lower resistive loads.  After that, anything down to 100 ohms will certainly do OK. When the load R gets lower than about ~10X the internal resistance of the cartridge, SQ starts to get dull (a subjective impression) and gain is measurably lost (a fact), because some signal voltage is lost to ground.  But the OP did not ask about any of this.

I recently used a 0.35mv Fuuga on the same Lamm LP2.1 + a Lamm L2.1 Ref and that combo was fine, but I would not go much lower in output.  Imo, moving coils delivering 0.25mv or less need more than 60dB of gain.

I believe Lamm could swap out the internal transformers for a pair yielding 30db for a total of 70dB gain.  If it were me, I'd look at a different cartridge.