[en] Following bombardment of a mesoporous silica sample by positrons ejected from a two-stage buffer gas trap, ortho-positronium (o-Ps) was emitted into vacuum with an efficiency of around 27%–28%. This ensemble, with a density close to 10¹¹ m⁻³, was then irradiated by multiple solid state-based laser beams up to 50 ns after positron implantation. Tunable over a wide range (230–2200 nm), the lasers have enabled excitation of the o-Ps Lyman-α transition, followed by subsequent excitation and, if desired, ionisation to vacuum. Excitation from the 2P state to intermediate states in the principal quantum number, $n_{\mathrm{P}\mathrm{s}}$, range $3⩽<!--\; ???\; -->n_{\mathrm{P}\mathrm{s}}⩽<!--\; ???\; -->18$ has been achieved with efficiencies ${\mathrm{ϵ<!--\; ??\; -->}}_{\mathrm{e}\mathrm{x}}^{n_{\mathrm{P}\mathrm{s}}}\gtrsim <!--\; ???\; -->80\mathrm{\%<!--\; \%\; -->}$, whilst the excitation efficiency of ground state o-Ps to the 2P state of ${\mathrm{ϵ<!--\; ??\; -->}}_{\mathrm{e}\mathrm{x}}^2\sim <!--\; ???\; -->13\mathrm{\%<!--\; \%\; -->}$ is currently limited by a mismatch between the Doppler broadening of the 1S-2P transition and the 225 GHz laser bandwidth at 243 nm. (paper)