The widely existing shallow decay phase of the X-ray afterglows of gamma-ray bursts (GRBs) is generally accepted to be due to long-lasting energy injection. The outflows carrying the injecting energy, based on the component that is dominative in energy, fall into two possible types: baryon-dominated and lepton-dominated ones. The former type of outflow could be ejecta that is ejected during the prompt phase of a GRB and consists of a series of baryonic shells with a distribution of Lorentz factors, and the latter type could be an electron-positron-pair wind that is driven by the post-burst central engine. We here provide a unified description for the dynamics of fireballs based on these two types of energy injection, and calculate the corresponding high-energy photon emission by considering synchrotron radiation and inverse Compton scattering (including synchrotron self-Compton and combined inverse-Compton) of electrons. We find that, in the two energy-injection models, there is a plateau (even a hump) in high-energy light curves during the X-ray shallow decay phase. In particular, a considerable fraction of the injecting energy in the lepton-dominated model can be shared by the long-lasting reverse shock since it is relativistic. Furthermore, almost all of the energy of the reverse shock is carried by leptons, and thus the inverse-Compton emission is enhanced dramatically. Therefore, this model predicts more significant high-energy afterglow emission than the baryon-dominated model. We argue that these observational signatures would be used to discriminate between different energy-injection models in the upcoming {\em Gamma-ray Large Area Space Telescope} (GLAST) era. ; Comment: 22 pages, 7 figures, accepted for publication in ApJ