We are using the STM32L476 and wanted to know if it is possible to use a 32.000kHz oscilator for the LSE input? If so is there any issues regarding using a different frequency then 32.768kHz?

[Tesla DeLorean]

You'd need to set the prescaler values appropriately. I haven't looked to see how the HSI/MSI might calibrate.

STM32 parts generally prefer the 6-7 pF crystals.

[MM..1]

Maybe you will have issue with RTC clock, but when you dont need RTC you can use it