Short answer
Do not put an LIR2032 in a device that names CR2032 unless the OEM explicitly allows a rechargeable coin. Higher voltage and different chemistry can damage electronics.
Only use LIR2032 when the device or OEM documentation names LIR / rechargeable coin explicitly.
What is the same
Roughly the same diameter and thickness class — they can look identical in a drawer.
What is different
CR2032: primary lithium manganese dioxide, ~3.0 V, not designed for recharge.
LIR2032: rechargeable lithium-ion, typically ~3.6–3.7 V nominal, lower capacity than primary CR2032, different duty cycle.
Do not use list
Do not treat LIR2032 as a “rechargeable CR2032.”
Do not confuse LIR2032 with ML2032 (another rechargeable class) or BR2032 (different primary lithium subclass).