  We present the first spectroscopic studies of the $C \ ^1\Sigma^+$ electronic
state and the $A \ ^1\Sigma^+$ - $b \ ^3\Pi_{0^+}$ complex in $^7$Li -
$^{85}$Rb. Using resonantly-enhanced, two-photon ionization, we observed $v =
7$, 9, 12, 13 and $26-44$ of the $C \ ^1\Sigma^+$ state. We augment the REMPI
data with a form of depletion spectra in regions of dense spectral lines. The
$A \ ^1\Sigma^+$ - $b \ ^3\Pi_{0^+}$ complex was observed with depletion
spectroscopy, depleting to vibrational levels $v=0 \rightarrow 29$ of the $A \
^1\Sigma^+$ state and $v=8 \rightarrow 18$ of the $b \ ^3\Pi_{0^+}$ state. For
all three series, we determine the term energy and vibrational constants.
Finally, we outline several possible future projects based on the data
presented here.
