The Fermi surface topology of the organic superconductor \lbets has been determined using the Shubnikov-de Haas and magnetic breakdown effects and angle-dependent magnetoresistance oscillations. The former experiments were carried out in pulsed fields of up to 60 T, whereas the latter employed quasistatic fields of up to 30 T. All of these data show that the Fermi-surface topology of \lbets is very similar to that of the most heavily-studied organic superconductor, \cuscn, except in one important respect; the interplane transfer integral in \lbets is a factor $\sim 10$ larger than that in \cuscn . The increased three-dimensionality of \lbets is manifested in radiofrequency penetration-depth measurements, which show a clear dimensional crossover in the behaviour of $H_{c2}(T)$. The radiofrequency measurements have also been used to extract the Labusch parameter determining the fluxoid interactions as a function of temperature, and to map the flux-lattice melting curve.