Invitations are basically infinite, but anyone that is invited is associated with the account of the person inviting them. If I invite someone, I will be responsible for them if they misbehave.
Trust is a two-way street. You will need to trust the person sending the invite with your email address. They will need to trust that you will be a contributing member of the community.
Edit: Who knew!? Account associations are public: https://lobste.rs/users
You can also join the irc chat room and participate/request an invitation: https://lobste.rs/chat
I'm going to look into this some more.