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You can look at the Texas Instruments MSP430 range, or the Microchip PIC16F91x range: Both of these have versions with 96-segment LCD drivers - plenty for a 4½ digit display. I don't think you'll find any that *specifically* drive a 4½ digit LCD.
Alternatively, there are plenty of chips (not MCU's) that will drive your display, depending on what you are designing. Maxim do timer/counters and ADC's that interface directly to LCD's.