  [abridged]
  Context: Very few examples of luminous blue variable (LBV) stars or LBV
candidates (LBVc) are known, particularly at metallicities below the SMC. The
LBV phase is crucial for the evolution of massive stars, and its behavior with
metallicity is poorly known. V39 in IC 1613 is a well-known photometric
variable, with B-band changes larger than 1mag. over its period. The star,
previously proposed to be a projection of a Galactic W Virginis and an IC 1613
red supergiant, shows features that render it a possible LBVc.
  Method: We investigate mid-resolution blue and red VLT-VIMOS spectra of V39,
covering a time span of 40 days, and perform a quantitative analysis of the
combined spectrum using the model atmosphere code CMFGEN.
  Results: We identify strong Balmer and FeII P-Cygni profiles, and a hybrid
spectrum resembling a B-A supergiant in the blue and a G-star in the red. No
significant Vrad variations are detected, and the spectral changes are small
over the photometric period. Our analysis places V39 in the low-luminosity part
of the LBV and LBVc region, but it is also consistent with a sgB[e] star.
  Conclusions: The radial velocity indicates that V39 belongs to IC 1613. The
lack of Vrad changes and spectroscopic variations excludes binary scenarios.
The features observed are not consistent with a W Virginis star, and this
possibility is also discarded. We propose that the star is a B-A LBVc or sgB[e]
star surrounded by a thick disk precessing around it.
  If confirmed, V39 would be the lowest metallicity resolved LBV candidate
known to date. Alternatively, it could represent a new transient phase of
massive star evolution, an LBV impostor.
