Does the paddle need to be soldered. If so, what should it be connected to?
Yes, for two reasons.
The paddle on the LFCSP package needs to be connected to the lowest potential of the part in questions. For single supply parts this would be ground. For bipolar supply parts (e.g. +/-15V) the paddle should be connected to the most negative voltage.
The paddle also needs to be soldered for mechanical robustness
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