Energies and probabilities of Lyman transitions of high rovibrationally excited H2, HD and D2 molecules have been measured and compared with calculations. The experimental results are obtained from laser-induced fluorescence spectra that have been recorded in the spectral range from 60 500 to 83 500 cm-1, covering 2/3 of the hydrogen Lyman band system. The necessary vacuum-UV radiation is produced by stimulated anti-Stokes Raman scattering, providing a widely tunable radiation source with narrow spectral bandwidth to resolve single Lyman transitions. The highest internal energies of detected hydrogen isotopologues are close to the dissociation limit. This extends the available data base of Lyman transitions from and to higher rotational states (J > 10) of HD and D2.