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

Revision:
0:368cfb35a89a
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/24_TFT_STMNUCLEO.lib	Fri Sep 28 03:37:23 2018 +0000
@@ -0,0 +1,1 @@
+http://os.mbed.com/users/cdtsilva/code/24_TFT_STMNUCLEO/#060b167a46ba