Any Software/Method to install LE when there's no SD slots on device?

It's possible, but there is a lot of work. First, that box is not officially supported either by U-Boot or Linux. You can hope that Tanix TX6 is compatible enough for it to work, otherwise you need to debug and fix any discrepancies. Then, you need to FEL boot U-Boot and somehow transfer LE image and write it to eMMC. I can think of two ways, maybe there is more:

1. setup network and transfer image into memory and then write it to eMMC

2. setup USB mass storage mode in U-Boot and write image directly to eMMC.

Both methods need special crafted U-Boot binary. LE U-Boot is stripped to the minimum to speed up boot process. It can be booted via FEL, but you won't get much useful features.

In any case, since it's unsupported TV box, you're on your own.