I would say, that the issue is not related to J-Link at all, but it is LPC1768 specific. Or maybe NXP’s LPCxxxx MCUs specific. I have built up Blackmagic Probe today in order to test different programmer/debugger. PlatformIO is capable to use this Blackmagic Probe without any problem for uploading as well as for debugging simple test program on STM32L053.
Trying uplod or debug on LPC1768 it doesn’t work.
another update, just to confirm, that my LPC1768 based board is OK, J-Link Lite is OK and the cables in between (as well as to PC) are OK too: I’ve created very simple program for LPC1768 within Em::Bitz. I’m able to run debugging session via my J-Link Lite and via the same SEGGER’s J-Link GDB server, I used for my attempts with PlatformIO - under Em::Bitz it works without problems.