Make these cuts from the 2x4:
12 pieces @ 29 inches x 3 inches x 1 1/2 inches
2 pieces @ 26 inches
Cut a piece of string 29 7/8 inches long and another 19 7/8 inches long.
Use each to trace a circle on the plywood one with a diamenter of 59 3/4 inches and one with a diameter of 39 3/4 inches. If you do it right, both can be drawn on the plywood without overlapping. Cut out the circles using the jigsaw.
Edgeband the circles.
Sand all surfaces.
Build the legs. Attach 4 pairs of (2) 29 inch long 2x4s so that they are flush on top, bottom and both sides. These are your legs.
Build the frame. Span the tops of the legs with the other (4) 29 inch 2x4s making a 35 inch square that stands 29 inches high. Make sure the spanning 2x4s are attached vertically (3 inche up and down), flush with the outside edges and the tops of the legs. Attach the (2) 26 inch long pieces in the middle for added support.
Attach the bigger circle to the top of the frame. Make sure it is centered on the frame.
Attach the lazy susan hardward to the bigger circle. Again, be certain that it is centered.
Attach the smaller circle to the top of the lazy susan hardware. You don't need to be reminded to make sure it is centered.
Fill in all holes with wood filler and sand smooth.
Paint or stain to your liking.
Give it a spin.