Need integrated for Tyler linbrook Signature

Might want to try a Portal Panache - use one with Linbrook System 2

I demoed my Jadis OR on the LS's and had no problem getting bass good response. These speakers are definetly tube friendly, provided the amp has high quality trans as does Jadis.
That would Cayin. Ck out their many models. Maybe the new Cayin 100, with 8 KT88 tubes. Abit over 2K but worth looking into. Besides you have a top class speaker, well worth over the asking price (fair value is $15K, Ty sells them for 1/3 the price), so you need a first class amp.
There's not many first class amps in the 2K range.
good luck

How about a BAT integrated.

I am driving mine right now with a VK200 and they sound great. I also have a Levinson No.29 at 50wpc and it works very well with my Linbrook Sigs.

I have a used Coda Ultra that was wonderful with the Linbrook Signatures. Moved on to separates recently, so if your interested let me know. You can go to the Coda Technologies website for more info on this well built and sonically pure integrated. Ty has used Coda with his speakers at previous audio shows so that should tell you he thinks it's a good match.

I've mated the same speakers with the McIntosh MA6900, Mac separates, Bel Canto and Cary SS separates, and the orginal Rowland Concentra, and to this day I greatly miss the Rowland - it was a magical combo (I'd think about going back if I wasn't doing multichannel). All that said, a big caveat is that when I had the Rowland I had a much better room, but I still believe it was a very synergistic combination. To this day I have not had better sound than that.