Lost mirror can be used to upgrade lens.(Lens is used to increase partner stars).The following are several ways to obtain a lost mirror.
Arcana
You can complete the arcana if you need a lost mirror. Since the arcana consists of many stages, it is possible that you can get many lost mirrors here. You can also have a chance to get ssr gear from arcana.
Summon
Summon will also give you lost mirror. The number of lost mirrors obtained depends on the partner grade. If you get R partner, you will get 10 lost mirrors
Event
You can buy a lost mirror at the Halloween event.You need 120 chocolates to buy 10 lost mirrors
Weekly reward
Clear all daily quest and claim weekly reward