The broccoli is going to flower and then go to seed. Once the heads are formed, harvest them and the plants will continue to produce side heads. Broccoli likes fertile soil.
Your lettuce did well because of the high nitrogen content of your soil. Fertilizer is rated %-%-%. The first number is nitrogen which is essential for green leaves. The next number is phosphorus which is for root growth such as carrots. The last number is potash which nourishes stems and the rest of the plant.
To find out what your soil needs contact your county Agriculture agent on how to get your soil tested. It might take 3 weeks or more. It probably will be too late for this season.
My thought is, for now, leave it alone, observe, and learn for next year.

Broccoli doesn't grow in NJ in the summer time. If you plant seeds now till the end of June and plant the plants into the garden between August first and labor day you should have some very nice broccoli by October until Thanksgiving. Broccoli loves shortening days and cool nights. In NJ its one of the best fall garden vegetables. Any variety will do... Bob.