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Method 1:

ans = Transpose[ Map[Thread, D[{f[x, y], g[x, y]}, {{x, y}}] /. {x -> lx, y -> ly}, 2], {2, 1, 3}]; MatrixForm /@ ans 

Method 2:

ans = MapThread[ Function[{x, y}, Evaluate@D[{f[x, y], g[x, y]}, {{x, y}}]], {lx, ly}]; 

Answer to original question

Your Jacobian matrix is constant. There's no need to evaluate it at many different points.

JacobianMatrix[{f[x, y], g[x, y]}, {x, y}] (* {{-10, 0}, {0, 8}} *) 

Note a common way to compute the Jacobian matrix is (search for Jacobian the docs for D):

D[{f[x, y], g[x, y]}, {{x, y}}]