Suggestion used tube amp between $1,500-2,000

Look for Cayin or VAS items, great value and great sound, new or used.  Most of its products are knock offs of vintage Mc, HK and Marantz designs, updated for SOTA parts.  I have purchased a few Cayin products and I found them better then stuff costing three and four times the price.

I'd echo John's recommendation of an integrated. The Cary Sli-80 build quality is excellent, it's easy to bias and gives you a large range of output tube options to tailor the sound to your liking. The small tubes and rectifiers are common types, meaning lots of choices in a wide range of prices. Having service and advice available within the U.S. is a bonus, as well. Most important, it sounds wonderful and is a pleasure to use.

Why buy used?
http://www.quicksilveraudio.com/products/midmono.html

I agree with the integrated option being a better bang in your budget range. They’re making a comeback for very good reasons many given above by John. A real problem can be finding the ideal preamp/amp/speaker interface that will suit you, it might prove hit and miss going forward. With an integrated your biggest concern is that the amp and speaker match up and that you’ll have enough power for your application and room size as noted.

The QS amps are great values and performers at their price and well beyond, I'll testify to that. The question is will the QS or any amp recommended be an ideal and satisfactory match to you with that LS7? 

For $2k, you can pick up a used Music Reference RM-200 (the original, not the Mk.2). It is well-suited for passive pre-amp use (input sensitivity, gain), so you can dispense with the LS-7 and get a better-sounding passive if you wish. Over twice the power of the good Quicksilver suggestion from yogiboy---100w at 8 ohms from only a pair of KT-88's per channel. And unlike any other tube amp with which I am familiar, more power into 4 ohms!