This information is applicable to MAX96705 and MAX9271.
From the datasheet it looks like some functions, such as the double clock rate input option (DBL) are not available when LCCEN is high (local control channel is enabled). Is this the case?
No. All functions are available regardless of the state of LCCEN.
LCCEN enables the local control channel of the part so that it can be programmed by a microcontroller. When this pin is high, functions are programmed by register. When this pin is low, there is no local control channel available to program the part, so pins (including those which would be used by the local control channel interface) are assigned to enable or disable functions.