the available formats depend on the underlying storage [1]. So you have to select the storage first! Note that you will need a file level storage to use qcow2.
I can do this: (In VM Settings) Hardware, Hard Disk (select) and click on Disk Aktion. I can only convert to qcow2 if i select the local storage Type: "dir" Storage.
LVM provides block level storage, so no, you can't. You could create an LV, format it with a file system (e.g.), and then mount that as directory-backed storage. However, I really can't recommend that.