  The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which
includes Minkowski 3-space, de Sitter 3-space, and Minkowski motion group is
considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family
has a solvable Lie group structure with left invariant metric. A generalized
integral representation formula which is the unificaton of representation
formulas for minimal timelike surfaces in those homogeneous Lorentzian
3-manifolds is obtained. The normal Gau{\ss} map of minimal timelike surfaces
in those homogeneous Lorentzian 3-manifolds and its harmonicity are discussed.
