You can pair your Logitech G903 LIGHTSPEED Wireless Mouse with any Logitech LIGHTSPEED USB Receiver (but not with other Logitech receivers, like the Bolt or Unifying receivers.)

To pair your mouse with a new receiver (of the correct type!) you would use the Logitech Connection Utility https://support.logi.com/hc/en-my/articles/360025141574 (or possibly also using Logitech G HUB as outlined in https://support.logi.com/hc/en-us/articles/7709072311959)

Logitech's receivers are not interchangeable.
They're either not-really-wifi or not-really-bluetooth, they won't link to anything except the 'family' they're designed for.

Logi change the dongle requirements over time. If you have an older keyboard & a newer mouse, even though they are supposedly "the same thing" they may be using different versions of the dongle technology. As far as I'm aware, nothing still uses the old Connect* software, which I think was for the receivers with a physical button. Later dongles were paired for life with the device they came in the box with, no mix & match at all. At least with the new Unifying dongles, you can manually pair several devices.

Thanks to roaima for the comment - there's a re-pairing utility Logitech Connection Utility available [for Windows only] which may help.

See How do Logitech keyboards coexist? What if I mix up the USB dongles? for how these 'mid-period' dongles worked.

*These days, there's 'Logitech Options', 'Set Point' and the newest 'Logi Options+', depending on hardware/OS.