Similar to what Alan said, most tv's now accept USB cards and can run a slide show without any additional device. Export your files from lightroom at 4k resolution and you'll find the file sizes are small and you can fit an incredible amount onto a USB. You may be able to run different directories (one at a time) on the TV if you want to differentiate your slide shows (waterfalls this afternoon, sunsets this evening, etc.). This is really an easy, inexpensive option.
If your TV can't handle this, I have found that many mid range and up DVD/Bluray players will accept and access a USB device, thus you can accomplish the same result that way, just keep in mind the resolution of the player.
Finally, you could update to a 4k player if you haven't already, and attach the USB to that. Prices have come down and more vivid displays and supporting 4k players which support enhanced colors are readily available.
I'll be interested in what option you choose.
Miles