The LP2 is a fine phonostage. If you like it, I believe you're on the right track to look for a cartridge that will work well with it. And the suggestion to consider a cartridge with .5mV or greater output is a good one. I'm currently auditioning a top caliber phonostage whose gain is the same as the LP2 (57.5dB) using a Shelter 901 that outputs .5mV. (This in comparison to my current phonostage reference which is a Pass Labs XONO that is solid state and offers flexible gain adjustment.) Let me just say I would be cautious about using a cartridge with a lower output than .5mV into a phonostage with much less than 56dB.
Cmk has given you sound advice and, imo, the impedence of your linestage is much less of an issue than gain and cartridge output. You might inquire of Lamm about a modification to the LP2's 40ohm load.
If you're unhappy with the Lamm, then changing your phonostage is certainly an option, but otherwise I would not look at it as the first thing to consider. If you were to look at other phono stages, as you note there are few tubed units with gain higher than 56-58dB. I am a strong fan of tube gear and, except for the XONO, my system is all tube yet I don't think having a solid state phono stage is a compromise. That's meant more as a comment on solid state phono stages as an option, not a judgement on the XONO. It is a bit surprising that both the LP2 and PH7 don't have balanced outputs.
(Sounds like you may be considering the Ref3, imo its an excellent choice for a linestage if balanced is a requirement.)
As to cartridges, the Allaerts MC1B and MC1 B MkII as Cmk mentioned, Shelter 90X, Lyra Titan, and Transfiguration W or Orpheus are a few to consider with output of .5mV or higher. You might search user systems at AA for the LP2 and see what cartridges its owners use.
Then there is consideration of how that cartridge mates with your tone arm wrt resonance frequency, which, for starters. means knowing the mass of the tonearm and the compliance of the cartridge.
Spec's can be a guide, but the best technical match is no assurance of audio happiness. At the end of the day, trust your ears and the connection you make with the music. Best of luck!