  We study here experimentally, numerically and using a lubrication approach;
the shape, velocity and lubrication film thickness distribution of a droplet
rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary
immiscible fluid and moves purely due to buoyancy. A low density difference
between the two mediums helps to operate in a regime with capillary number $Ca$
lying between $0.03-0.35$, where $Ca=\mu_o U_d /\gamma$ is built with the
surrounding oil viscosity $\mu_o$, the droplet velocity $U_d$ and surface
tension $\gamma$. The experimental data shows that in this regime the droplet
velocity is not influenced by the thickness of the thin lubricating film and
the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional
numerical results of the film thickness distribution agree well with each
other. The mean film thickness is well captured by the Aussillous & Qu\'er\'e
(2000) model with fitting parameters. The droplet also exhibits the
''catamaran'' shape that has been identified experimentally for a
pressure-driven counterpart (Huerre $\textit{et al}$. 2015). This pattern has
been rationalized using a two-dimensional lubrication equation. In particular,
we show that this peculiar film thickness distribution is intrinsically related
to the anisotropy of the fluxes induced by the droplet's motion.
