I would like to have a function which will write to the appropriate I2C LCD based on a functions "String" input parameter. I'm having trouble determining how to code it correctly.
Because you can't.
Names are converted to addresses when the compiler runs. There is, in the hex file uploaded to the Arduino, nothing called LEFT_lcd.
You certainly can't call methods based on the name of the object.
You could keep track of names and addresses in a struct, and, in the function, convert the name to an address. Iterate through the struct, comparing the passed in name to the stored name, and use the address in the position that corresponds to that of the name in the struct.
But, why bother. It would be simpler to create the objects in the first order, and use numbers (0, 1, 2 or #define statements).
Or, create an array of objects, and pass the index to the function that cares.