Assuming that you are referring to a character-type LCD rather than a graphical LCD, I would recommend you use a standard AVR and select an off-the-shelf LCD (preferreably one that uses a HD44780 LCD controller) that has the number of characters you need for your design. This will give you more flexibility for future design upgrades.
A "LCD" type uP will have stuff inside to drive a LCD directly. It would be easier to follow hgmjr's suggestion and use an LCD that has built-in HD44780 controller.