In the country as a whole, June gets around 22,000 international overnight arrivals. That makes June twice as busy as September but one-third less busy than March.
Though San Pedro is always busy compared with the rest of the country, on average about half of the hotel rooms are vacant on a given night, so you can always find something. Off-season you may also get a better deal as a walk-in.
That being said, for a specific hotel especially during an event period such as Lobsterfest, it's a good idea to book ahead.