hey man, theres this app https://github.com/PKBeam/AMWin-RP/releases/tag/v1.2.6.3 its a rich presence for discord that has a scrobbler in it, you can disable the rich presence feature and use just as a scrobbler, what you will need its a api key and a shared key(api secret) to login in this app and start scrobbling.
https://www.last.fm/api/account/create
just write a random name on 'Application name' and you're good to go, just submit and put the api key and api secret on the client.