First off, I have not heard the Lyra, so no comment there.
I have heard the Koetsu RSP a year or so ago, (in my friend's system, which I know quite well, and which is better than my own, btw), and it is highly resolving, and incredibly musical, but it does lack a bit of bass frequency extension. (And, if you like your mid-range to be somewhat lush, this just might be the cartridge for you.) If you go with this you would probably not be sorry, (except for having to pay the ridiculous tariff on new cartridges here in the US!).
I currently own the Dynavector XV-1S (I got it used a couple of months ago), after having had various other cartridges, (including the Koetsu Rosewood Signature (albeit the non-platinum version), and the Shelter 90X). The XV-1S has the frequency extension of the Shelter (but even slightly more refined, IMHO), and the incredibly low noise floor of the Koetsu. The Dynavector also is very neutral, (the Koetsu is very warm, and the Shelter is somewhat warm), and it is highly resolving (more so than the Rosewood Signature, and at least on par as the RSP in resolution, (and I think a bit more resolving, but that is based on sonic memory from a year or so ago, so take that with a grain of salt.) The soundstaging and imaging is incredible, on par with the best I have ever heard, and it is better than either the Shelter or the Rosewood Signature. (I'll be honest and state I can not recall how good the Koetsu RSP was at this. My guess is that they are on par.) I think this is the cartridge I will be using for the next few years, at least. (Yea! No more yearly auditions of phono cartridges. Now on to the upgrade of my turntable or my speakers! Almost done!)
My two cents worth, and I hope this helps.
PS An acquaintance, here on Audiogon, has recently upgraded from the Dynavector XV-1S to the Clearaudio Goldfinger V2, and he says that it is slightly more resolving, and has a slightly lower noise floor. (However, the $10K price tag might be an obstacle for some people. Yikes!)