The three-dimensional Heisenberg group H3 has three left-invariant Lorentz metrics g1, g2
Nearby in the stack
and
g3
. They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric
g1
as a Lorentz Ricci soliton. This Ricci soliton
g1
is a shrinking non-gradient Ricci soliton. Likewise we prove that the isometry group of flat Euclid plane E(2) and the isometry group of flat Lorentz plane E(1,1) have Lorentz Ricci solitons.