You cannot delete your posts in the forum.
A moderator, however, can.
If you want a (some) post(s) to be deleted, simply report them!
You can do so by reporting yourself...lichess.org/report
Just paste the links of the posts (and the post number) in the report.
Note that if it's the first post of a nice/important/long thread, deleting the post will delete the entire thread, so provide a decent reason as to why you'd like to delete it.
Other than that, that's all.