We　consider　the　inviscid　limit　of　the　two-dimensional　viscous　lake　equations　when　the　Navier　slip　conditions　are　prescribed　on　the　impermeable　boundaries　of　the　general　regular　domains.　Our　results　show　that　the　boundary　layer　of　the　viscous　lake　equations　with　Navier　boundary　is　always　nonlinearly　stable　in　some　Sobolev　spaces　and　we　justify　an　asymptotic　expansion　which　involves　a　weak　amplitude　boundary　layer,　with　the　same　thickness　as　in　asymptotic　theory　and　a　linear　behavior.