What size pilot hole for 516 lag screw?

Answer 1

You should use a bit that is just a little bit smaller, but only drill the depth about 2/3 of the distance. This will allow solid penetration into the undrilled wood. 5/16 lags = 3/16 or 1/4 pilot drill bit.

Answer 2

For a 5/16” should be 9/32.