We present a detailed study of the 2016 eruption of nova V407 Lupi (ASASSN-16kt), including optical, near-infrared, X-ray, and ultraviolet data from SALT, SMARTS, SOAR, Chandra, Swift, and XMM-Newton. Timing analysis of the multiwavelength light-curves shows that, from 168 days post-eruption and for the duration of the X-ray supersoft source phase, two periods at 565 s and 3.57 h are detected. We suggest that these are the rotational period of the white dwarf and the orbital period of the binary, respectively, and that the system is likely to be an intermediate polar. The optical light-curve decline was very fast ($t_2 leq$ 2.9 d), suggesting that the white dwarf is likely massive ($gtrsim 1.25$ M$_{odot}$). The optical spectra obtained during the X-ray supersoft source phase exhibit narrow, complex, and moving emission lines of He II, also characteristics of magnetic cataclysmic variables. The optical and X-ray data show evidence for accretion resumption while the X-ray supersoft source is still on, possibly extending its duration.
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