  Cadenced optical imaging surveys in the next decade will be capable of
detecting time-varying galaxy-scale strong gravitational lenses in large
numbers, increasing the size of the statistically well-defined samples of
multiply-imaged quasars by two orders of magnitude, and discovering the first
strongly-lensed supernovae. We carry out a detailed calculation of the likely
yields of several planned surveys, using realistic distributions for the lens
and source properties and taking magnification bias and image configuration
detectability into account. We find that upcoming wide-field synoptic surveys
should detect several thousand lensed quasars. In particular, the LSST should
find 8000 lensed quasars, 3000 of which will have well-measured time delays,
and also ~130 lensed supernovae, which is compared with ~15 lensed supernovae
predicted to be found by the JDEM. We predict the quad fraction to be ~15% for
the lensed quasars and ~30% for the lensed supernovae. Generating a mock
catalogue of around 1500 well-observed double-image lenses, we compute the
available precision on the Hubble constant and the dark energy equation
parameters for the time delay distance experiment (assuming priors from
Planck): the predicted marginalised 68% confidence intervals are
\sigma(w_0)=0.15, \sigma(w_a)=0.41, and \sigma(h)=0.017. While this is
encouraging in the sense that these uncertainties are only 50% larger than
those predicted for a space-based type-Ia supernova sample, we show how the
dark energy figure of merit degrades with decreasing knowledge of the the lens
mass distribution. (Abridged)
