Most of the time this issue is caused by insufficient permissions for the user specified in the LaunchPoint Service under "Admin > LaunchPoint." This article mentions what is required for LinkedIn lead gen forms to work on LinkedIn for the user, this is not for Marketo but it makes a great reference.
For Marketo, we require full permissions for the integration to work.
- Campaign Manager OR Account Manager (The integration user will only be able to have one of these permissions)
- Company Page Admin
- Lead Gen Forms Manager
Ensure that the user has all 3 permissions. If you made some changes to the permission, re-authorize LaunchPoint service and, try again. I would also recommend deleting and re-creating the LaunchPoint service. It is recommended every time you make changes to the permission so that the connection works without any issue. You could see the form in Marketo after this step.
If any one of the permissions is added later, I recommend creating a test lead on the form referring the document - https://www.linkedin.com/help/lms/answer/94217. The leads that fill out the form after this step would be found on Marketo. You could List Import the other leads that filled out the form.
If you are still facing the issue after verifying the above steps, please raise a support ticket with Marketo. We could verify whether the issue is with Marketo or the Integration itself.