Does my 2015 MacBook 12" produce 4K on the LG UltraFine 4K Display Does my 2015 MacBook 12" work with the LG UltraFine 4K Display and does it actually produce 4k picture?
Hard to tell about your hardware since it could have issues, but that hardware in general supports 4K in general and in specific for the LG display that Apple sells directly. 


https://support.apple.com/kb/HT207447
https://support.apple.com/en-us/HT206587


I’ve happily used that model Mac for almost 3 years now and my LG 4K display has been awesome first came out and I bought it.