What the 125°C rating buys you
Memory and analog — what's on the die
The 2 KB of EEPROM on-chip is a genuine differentiator: you can store calibration constants, serial numbers, or configuration parameters without adding an external 25LCxxx part, which saves board space and one SPI bus. The 16-channel 12-bit ADC and single 12-bit DAC cover most sensor-input and analog-output needs for a control loop or data-acquisition front end. If your design needs more than 51 GPIOs, you'll need to step up to a larger package variant.
The internal oscillator means you can skip the external crystal if the timing accuracy requirements are loose, but for USB operation you'll still want a resonator or external clock.
ST continues to manufacture the STM32L0 family, and the STM32L053R8T3 remains a current catalog item.