We perform a systematic analysis of the conditions under which generalized gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space dimensions. By the term generalized, we mean that the dynamics of the concerned fields is governed by Lagrangian densities which are general functions of the quadratic field invariants, leading to physically consistent models. The analysis defines exhaustively the class of this kind of Lagrangian models supporting those soliton solutions and leads to methods for their explicit determination. The necessary and sufficient conditions for the linear stability of the finite-energy solutions against charge-preserving perturbations are established, going beyond the usual Derrick-like criteria, which only provides necessary conditions.