When starting my LC, there is a high pitch screech sound for around two seconds.

Suspect drive belt slipping.. Have drive belt and components checked... Extra load is put on belt momentarily when engine is started as alternator replenishes battery voltage that was drained during cranking .. Belt squeal/screeching for a couple seconds as engine starts is common on all vehicles when belt tension is incorrect or belt is worn .. Noise can occur intermittently as engine starts.