Lake Lavon is really a mud whole. No beaches you can pull a boat up to.
Go up to Ray Roberts, launch at Isle du Bois and head toward the dam. just before you get to the dam on the left hand side (east side) is a small cove with sand and some rock. You can beach your boat there. I spent many a Sunday afternoon there with another boating family.
+1, Ray Roberts would be a much better choice. Lavon has man made beaches at Collin and Mallard that were actually pretty nice at one time. You have to pull you boat up to the side because they are buoyed off. I went to Avalon a lot when in high school and it has never had a good beach. Texoma is my favorite the islands are an excellent place to go. Even in a fairly stout south wind you can launch at Loes and be ok. There are also some real nice spots in the Little Mineral arm. Launch at Grand Pappys. Not sure about water clarity on Texoma right now. It might be the color of the Red River.