Hmm... Honestly, tube amps will have pretty hard time driving LAT-1000s. Lowest point in LAT-1000 impedance curve is around 2ohms(!!) in bass region, this will rull out most of the tube amps.
BTW, LAT-1000 nominal impedance is 3ohms...
But, if you still decide to drive them with tube amp then there are only few of them on the market that are powerfull and capable to drive tough loads:
-Audio Research Reference 610T(they are powerfull enough)
-CAT JL3 Signature
-VTL Siegfried's
Forget about OTLs, low power tubes or SE tubes. They are not capable to drive LAT-1000.