No, different company.

LEX is lazada's in-house courier service. Usually no tracking number is provided unless requested (need to call customer service).

Hong Kong set should be global set = Malaysia set. Not China version so no worries about hardware. I remember some ppl mentioned at Mi Malaysia's fb that they received HK set as well when they bought from Mi Malaysia website.

Now about warranty, there is some issue. Some ppl commented/reviewed at Lazada page (not sure if Lazada had screen them off already, can't seem to find them), that they checked the imei number with Mi Malaysia service centre and they confirmed it is original global version but not under their warranty. Which is contrary to what Lazada claim.

So now if you are not too concerned with warranty (you can just get back to lazada in case anything happen), the device is fine, hardware and software wise.

I bought my Mi4 under Mont Asia distribution, who is authorised by Xiaomi to bring into Malaysia. My set is covered by Mi Malaysia warranty, although on the box stated it is India set lol

Yes, they can check based on the phone's IMEI number.

Many users said the battery life becomes better after updating to latest stable ROM (even without rooting).