  Both lucky imaging techniques and adaptive optics require natural guide
stars, limiting sky coverage, even when laser guide stars are used. Lucky
imaging techniques become less successful on larger telescopes unless adaptive
optics is used, as the fraction of images obtained with well behaved turbulence
across the whole telescope pupil becomes vanishingly small.
  Here, we introduce a technique combining lucky imaging techniques with
tomographic laser guide star adaptive optics systems on large telescopes. This
technique does not require any natural guide star for the adaptive optics, and
hence offers full sky-coverage adaptive optics correction. In addition, we
introduce a new method for lucky image selection based on residual wavefront
phase measurements from the adaptive optics wavefront sensors.
  We perform Monte-Carlo modelling of this technique, and demonstrate I-band
Strehl ratios of up to 35% in 0.7~arcsecond mean seeing conditions with 0.5~m
deformable mirror pitch and full adaptive optics sky-coverage. We show that
this technique is suitable for use with lucky imaging reference stars as faint
as Magnitude 18, and fainter if more advanced image selection and centring
techniques are used.
