7-segment output: 4-6V, LCD input: 3-5V. How to convert?
If the LCD is the "wide voltage" version which can handle up to 5V, simply run both the LCD and the positive rail of the ADC from 5V.

If it's the 3V version, then this is probably not a good idea (although the LCD datasheet is typically unhelpful on range/abs max details) and either dropping the ADC positive rail to 3V (if possible, I haven't checked the datasheet to see if this is in spec) or changing ADC to a lower voltage version would be options.
The other option as you mention is to use voltage dividers (or level shifter ICs, etc) on the outputs of the ADC to drop the 0-5V down to 0-3V. This is cheap and easy but will add a lot of components to your board.  

Unless you are absolutely stuck on using this LCD and ADC combo, I would probably look at making the LCD and ADC run from the same rail (i.e. swapping one or both if necessary)