  This paper deals with the Lipschitz regularity of minimizers for a class of
variational obstacle problems with possible occurance of the Lavrentiev
phenomenon. In order to overcome this problem, the availment of the notions of
relaxed functional and Lavrentiev gap are needed. The main tool used here is a
ingenious Lemma which reveals to be crucial because it allows us to move from
the variational obstacle problem to the relaxed-functional-related one. This is
fundamental in order to find the solutions' regularity that we intended to
study. We assume the same Sobolev regularity both for the gradient of the
obstacle and for the coefficients.
