  We construct 1/4 BPS, threshold F-D$p$ bound states (with $0\leq p \leq 5$)
of type II string theories by applying S- and T-dualities to the D1-D5 system
of type IIB string theory. These are different from the known 1/2 BPS,
non-threshold F-D$p$ bound states. The near horizon limits of these solutions
yield Lifshitz-like space-times with varying dynamical critical exponent
$z=2(5-p)/(4-p)$, for $p\neq 4$, along with the hyperscaling violation exponent
$\theta = p - (p-2)/(4-p)$, showing how Lifshitz-like space-time can be
obtained from string theory. The dilatons are in general non-constant (except
for $p=1$). We discuss the holographic RG flows and the phase structures of
these solutions. For $p=4$, we do not get a Lifshitz-like space-time, but the
near horizon limit in this case leads to an AdS$_2$ space.
