Initiate the conversation yourself. YOU can ask for an updated lease, for the time period you desire.
I would not do this, partly based on my own experience.
Read up on state/city tenant law. In some places the window has already passed for raising your rent effective June 14. Once May 14 or 15 passes, LL's next opportunity may pass to July. Of course this is a two-way street and you are obligated to pay the rent for the extra month.
Then if LL comes to you on, say, June 1 asking you for an increase that sounds high, let him know your understanding of law and from this negotiate. "I understand I'm in until August 14 at the same rent, but how about we go two years from June 14 with a $25 increase [instead of the $50 you want]?"
In any event, most places in the US work on AT LEAST one-month lead times when everything is factored in, LLs hate turnover and Newton's First Law says inertia governs most things. You want intertia (want to stay there), so you are in the position of strength.
It only sounds scary if you haven't tried it.