We present the first spectroscopic studies of the $C ^1Sigma^+$ electronic state and the $A ^1Sigma^+$ - $b ^3Pi_{0^+}$ complex in $^7$Li - $^{85}$Rb. Using resonantly-enhanced, two-photon ionization, we observed $v = 7$, 9, 12, 13 and $26-44$ of the $C ^1Sigma^+$ state. We augment the REMPI data with a form of depletion spectra in regions of dense spectral lines. The $A ^1Sigma^+$ - $b ^3Pi_{0^+}$ complex was observed with depletion spectroscopy, depleting to vibrational levels $v=0 rightarrow 29$ of the $A ^1Sigma^+$ state and $v=8 rightarrow 18$ of the $b ^3Pi_{0^+}$ 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.
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