Is it possible to lower estrogen level by going on an antiestrogen diet to increase testosterone?

Maybe: First, it depends upon what you mean by 'anti-estrogen' or 'anti-estrogenic' diet. Second, it depends upon how closely & stringently you follow it. Next, you should check your levels several times before starting (results will vary so average them). Finally, no peer-reviewed studies have demonstrated any benefit in randomized controlled trials but it appears safe & healthy enough.