You need some intelligence between the Lepton and the LCD display. Code running on this device needs to read data from the Lepton via its VoSPI interface, convert it into an image (RGB data) and then push it to the LCD display via another SPI interface. Conversion of the radiometric data from the Lepton to a RGB image generally requires scaling it into a set of 8-bit values and then using those to index a false-color palette lookup to get RGB values for display. The VSYNC signal on the breakout board must be enabled by sending a command to the Lepton via its I2C CCI interface. VSYNC is used to notify an external device there is a frame available to read. Reading the VoSPI interface is not trivial although there is a lot of code out there on the internet showing how. Minimum requirements are probably a 32-bit processor with > 32 kB of RAM. An Arduino won't cut it.
People have used boards like the Raspberry Pi with both the raw Lepton breakout board and the USB UVC capable PureThermal boards but the Pi is a bit heavy (linux) for a simple display.
What might interest you is Damien Walsh's build:
https://damow.net/building-a-thermal-camera/. He used an ESP32.
And if you want to see various approaches I took over the years:
https://github.com/danjulio/lepton. I made a camera with a LCD display called tCam too (
https://github.com/danjulio/tCam/tree/main/tCam)
Interestingly the PureThermal firmware (at least the source) seems to have some code related to displaying on an LCD but I'm not sure that's enabled and I've never seen one directly connected to a LCD. You might check out the firmware repository though:
https://github.com/groupgets/purethermal1-firmwareFinally, search github. There are a lot of projects (of varying capability and completeness...).
Good luck! Thermal imaging is very cool.