  In order to probe a possible time variation of the fine-structure constant
($\alpha$), we propose a new method based on Strong Gravitational Lensing and
Type Ia Supernovae observations. By considering a class of dilaton runaway
models, where $\frac{\Delta \alpha}{\alpha}= - \gamma \ln{(1+z)}$, we obtain
constraints on $\frac{\Delta \alpha}{\alpha}$ at the level $\gamma \approx
10^{-2}$ ($\gamma$ captures the physical properties of the model). Since the
data set covers the redshift range $0.075 \leq z \leq 2.2649$, the constraints
derived here provide independent bounds on a possible time variation of
$\alpha$ at low, intermediate and high redshifts.
