Can any compound be a Lewis acid but not be a Brønsted acid?
Certainly.  There are many compounds that can accept a pair of electrons from a Lewis base, yet don't have any Brønsted-Lowry acid (proton) moiety. The two are really rather different things, although there are of course many compounds that are both Lewis and Brønsted-Lowry acids ($\ce{Al(OH)3}$ for example).  

Some examples of Lewis acids that are not also Brønsted-Lowry include:  

$\ce{BF3}$
$\ce{(CH3)3B}$
$\ce{AlCl3}$
Metal cations like $\ce{Li+}$, $\ce{Na+}$, $\ce{Mg^2+}$, etc.