I've booked flights with them twice (to cut a long story short I previously lived in China and still have money in my WeChat wallet that I wanted to use up - you can search and pay directly via WeChat witgh LY.com - this is the only reason I booked with them).
For the two flights I booked I found that LY.com had the best price available compared to Skyscanner etc. The first time I booked I admit I did it half expecting to never see the money or to hear from them again, but it was fine.
They are a legitimate company and have an international Corporate Travel arm from what I discovered.
However 1) if there is a problem or you want to chase things (like add seat selection etc) it can be difficult to resolve (they are in China) and 2) if you use them to book a budget airline whereby you need to print boarding passes online, you wont be able to login to the airline website to print the tickets as LY.com use their own email address to register the booking and good luck getting that off them.
However, I didn't book budget airlines, my itinerary (with airline booking code) was emailed to me within 15 minutes and I had no problems whatsoever.