  The $^7$Li abundance calculated in BBN with the baryon-to-photon ratio fixed
from fits to the CMB power spectrum is inconsistent with the observed lithium
abundances on the surface of metal-poor halo stars. Previous cosmological
solutions proposed to resolve this $^7$Li problem include photon cooling
(possibly via the Bose-Einstein condensation of a scalar particle) or the decay
of a long-lived $X-$particle (possibly the next-to-lightest supersymmetric
particle). In this paper we reanalyze these solutions, both separately and in
concert. We also introduce the possibility of a primordial magnetic field (PMF)
into these models. We constrain the $X-$particles and the PMF parameters by the
observed light element abundances using a likelihood analysis to show that the
inclusion of all three possibilities leads to an optimum solution to the
lithium problem. We deduce allowed ranges for the $X-$particle parameters and
energy density in the PMF that can solve $^7$Li problem.
