It's very hard to make that call not knowing which Lyra cartridge you are describing. The Lyra Clavis da Capo was a bright and a bit thin sounding cartridge, nothing like the cartridges described above. Other Lyra carts of that general vintage are similarly voiced. The more modern Lyra carts have a bit warmer tonal balance but still have that characteristic bright / thin sound that brings out (exaggerates?) so much musical detail.
I can't think of ANY Lyra cart that sounded like ANY Koetsu cart I've heard. Likewise, I would never compare the sound of a Lyra cart to a Shure cart. No tonal similarity whatsoever.
Generally speaking, Denon and Audio Technica carts are warmer and a bit less refined than the Lyras.
Can't comment on the latest offerings from other manufacturers since I do not have broad experience with them.
If I were looking for a nice performing cart for a good price, I'd consider an Audio-Technica 33PTG/II (not available in the states, but less than $500 from eBay out of Japan or HK), or an AT-OC9/II or III (II being my personal preference). Particularly, the OC9 is a bit tilted up but warmer than the Lyras (I have owned and used both Lyra and OC9s in my system).
Another option would be to get a Denon DL-103 (or 103R) cart that has been retipped and upgraded by SoundSmith. Those are supposed to be quite good performers with a slightly tilted-up tonal balance (compared to stock Denon 103s). The modified units are more expensive than the AT carts mention above. I have not owned nor heard the SoundSmith modifications, but get this information from those whose opinions I trust.
OK, now I'm heading off to put on my flame-proof Kevlar underwear and armor.
:)
.