Hey we host on heroku so i know my way around it a bit. It looks like you can use this buildpack for common lisp.

To use a specific buildpack in your heroku app, go to the settings for your heroku app on the web administration tool, to "Buildpacks," click "Add Buildpack," and just paste in the URL of the buildpack's git repo. When you push your code to heroku it'll grab from the buidlpack's git repo and use the instructions there to set up your application. I think there's also a way to add a buildpack via terminal but i forgot it :P

Make sure you follow the readme of the buildpack and copy the example git project as a base to work from. It'll contain important files (notably Procfile) for heroku to use to build off of.

I haven't actually tried any of this so I don't know if here are any other potential issues but in theory this is how you'd do it. Good luck!