One of the classical problems concerning the peg solitaire game is the feasibility issue. Tools used to show the infeasibility of various peg games include valid inequalities, known as pagoda-functions, and the so-called rule-of-three. Here we introduce and study another necessary condition: the solitaire lattice criterion. While the lattice criterion is shown to be equivalent to the rule-of-three for the classical English 33-board and French 37-board as well as for any m×n board, the lattice criterion is stronger than the rule-of-three for games played on more complex boards. In fact, for a wide family of boards presented in this paper, the lattice criterion exponentially outperforms the rule-of-three.