Convex lattice polygon is said to be optimal in sense of $l_p$ metric if its $l_p$-perimeter is minimal with respect to the number of its vertices. In this paper, the asymptotic expression for the Euclidian perimeter of optimal convex lattice $2k$-gons is derived as a function of the number of its vertices. The optimality is taken in sense of $l_p$ metric for every integer $p$, and also for $p=\infty4$.