setting display range off ICL7107
You don't need an op-amp, in fact many op-amps will add excessive error. The 710x series has fully differential inputs, which you can take advantage of. 

Assuming you want to stay with a 100mV reference, divide the input down so that the span is 150mV. That is a ratio of (4.45-0.42)/0.15 = 26.87:1. Move the decimal point behind the 2nd LSD. 

At this point it will read 165.6 with 4.45V in and 15.6 with 0.42V in. You need to apply an offset voltage of +15.6mV to the "In Lo" terminal relative to COM, assuming your input is applied relative to COM as well. This is easy to do if your reference is also relative to COM. 







simulate this circuit &ndash; Schematic created using CircuitLab

With the (negative) offset added, the display will show bbb.0 for  0.42V in and 150.0 for 4.45V in, ideally. You may need to adjust two of the ratios with trimpots (say adjust R2 AND R4 or R2). First adjust R7 to get zero display with 420mV in, then adjust the full scale to 150.0 with 4.45V in. 



Another plan would be to rejig the display to use a 2V span (1.00V reference), which would involve also changing the autozero and integration caps/resistor. This would yield less noise in the display and maybe a bit less drift.