Magic mouse for older iMac

No.

Please review the Tech spec’s and Compatible at > https://store.apple.com/xc/product/MMMQ3AM/A

Personally I would just get and use an inexpensive USB Logitech or Generic mouse to use with an older iMac running Lion.

Might be better off with one that uses a USB Receiver, since Lion did not have very advanced Bluetooth...

https://www.amazon.com/wireless-mouse/s?k=wireless+mouse