There are many examples on MBED for ST7735 controlled LCDs, but they're mostly for the AdaFruit LCD. This is a working example of the library used for the cheap-as-dirt KMR-1.8 SPI 128x160 TFT LCD, on a "Black Pill" STM32F407VE developement board.

Dependencies:   24_TFT_STMNUCLEO mbed