  Nova LMC 2009a is confirmed as a Recurrent Nova (RN) from positional
coincidence with nova LMC 1971b. The observational data set is one of the most
comprehensive for any Galactic or extragalactic RN: optical and near-IR
photometry from outburst until over 6 years later; optical spectra for the
first 6 months, and Swift satellite Ultraviolet and X-ray observations from 9
days to almost 1 year post-outburst. We find $M_V =
-8.4\pm0.8_{\mathrm{r}}\pm0.7_{\mathrm{s}}$ and expansion velocities between
1000 and 4000 km s$^{-1}$. Coronal line emission before day 9 indicates shocks
in the ejecta. Strengthening of He II $\lambda$4686 preceded the emergence of
the Super-Soft Source (SSS) in X-rays at $\sim63-70$ days, which was initially
very variable. Periodic modulations, $P=1.2$ days, most probably orbital in
nature, were evident in the UV and optical from day 43. Subsequently, the SSS
shows an oscillation with the same period but with a delay of 0.28P. The
progenitor system has been identified; the secondary is most likely a sub-giant
feeding a luminous accretion disk. Properties of the SSS infer a white dwarf
(WD) mass $1.1 \mathrm{M}_\odot \lesssim M_{\rm WD} \lesssim 1.3
\mathrm{M}_\odot$. If the accretion occurs at constant rate, $\dot{\it{M}}_{\rm
acc} \simeq 3.6^{+4.7}_{-2.5} \times 10^{-7} \mathrm{M}_\odot$ yr$^{-1}$ is
needed, consistent with nova models for an inter-eruption interval of 38 years,
low outburst amplitude, progenitor position in the color-magnitude diagram, and
spectral energy distribution at quiescence. We note striking similarities
between LMC 2009a and the Galactic nova KT Eri, suggesting that KT Eri is a
candidate RN.
