Linear systems on Lie groups are a natural generalization of linear systems on Euclidian spaces. For such systems, this paper studies what happens with the outer invariance entropy introduced by Colonius and Kawan [SIAM J. Control Optim., 48 (2009), pp. 1701-1721]. It is shown that, as for the linear Euclidean case, the outer invariance entropy is given by the sum of the positive real parts of the eigenvalues of a linear derivation D that is associated to the drift of the system.