As a ballpark estimate, when using a MCU to emulate logic without the assistance of a slave bus interface peripheral, expect to need two orders of magnitude more instruction cycles per second than the logic clock speed. Coromonadalix's suggestion of a Teensy should be capable of doing the job.
However, the display output of an 8279 has considerably relaxed timing vs its CPU interface, with each multiplexed digit valid for 490us after the rising edge of /BD, so if you keep the 8279, and capture its A0:3, B0:3 and S0:3 outputs in an ISR triggered by /BD rising edge, just about any MCU can do the job. You don't actually need all of S0:3 as you just need to detect the first digit in the multiplexing sequence, so if you are short of MCU pins, monitor S0 for decoded mode, and S3 transitioning high to low for encoded mode, which brings it within reach of an ordinary Arduino Uno or Nano, with an I2C LCD.