  Using Lakshmibai-Seshadri paths, we give a combinatorial realization of the
crystal basis of an extremal weight module of integral extremal weight over the
quantized universal enveloping algebra associated to the infinite rank affine
Lie algebra of type $B_{\infty}$, $C_{\infty}$, or $D_{\infty}$. Moreover, via
this realization, we obtain an explicit description (in terms of
Littlewood-Richardson coefficients) of how tensor products of these crystal
bases decompose into connected components when their extremal weights are of
nonnegative levels. These results, in types $B_{\infty}$, $C_{\infty}$, and
$D_{\infty}$, extend the corresponding results due to Kwon, in types
$A_{+\infty}$ and $A_{\infty}$; our results above also include, as a special
case, the corresponding results (concerning crystal bases) due to Lecouvey, in
types $B_{\infty}$, $C_{\infty}$, and $D_{\infty}$, where the extremal weights
are of level zero.
