I lived in Lavallette. It's 99% street parking and it's free. First come first served. There is no local resident access in Lavallette. Anyone can get a badge and anyone can access the beach. The badge gets you on the beach not where you live.
In theory, the beaches are open to the public there. As a practical matter, however, it discourages most of the public from accessing local beaches. We rode our bicycles as far north as Point Pleasant and as far south as Seaside Heights. I did not see any large public parking lots except in Point Pleasant and Seaside Heights. Sporadic street parking several blocks from the beach discourages the public from accessing many of the beaches in Lavallette.