Your L. fargesii may still be small, but it looks a lot healthier than most pics I've seen. Mine was a bulb from Chen Yi a decade ago. Had it for 3-4 years when it first flowered. It looked like the pics I usually see:
This is what you have to look forward to:
Yes, mine was in full sun (with mulch, of course), although I think it would have preferred some shade. Most years, the top would die back in mid to late summer. In my clay based soil, the bulb rotted one year during a particularly wet summer. Same with my L. taliense var. kaichen. It had 12 blooms that year.