Hi Zhiwei:
Your lauterbach T32 version may not work with HSE_DEMOAPP_S32K3X4_0_1_1_0.
Below is the flash bin file I found in the new version of T32(C:\T32\demo\arm\flash\long)

And the old version, which can only use HSE_DEMOAPP_S32K3XX_0_0_8_3.

I upload the S32K3x2.bin and S32K3x4.bin , you can try copy that to your folder, or use the HSE_DEMOAPP_S32K3XX_0_0_8_3 first for learning.
BR.
Haibing.Zeng