Dear Community,
"The functions implemented at the SDK for LPSPI do not have "native support" for 3-wire. So it required to make some changes to support half duplex mode." according to this sentence I have changed to support half duplex mode. I changed to support half duplex mode these functions LPSPI_DRV_MasterInit(..), LPSPI_SetPinConfigMode(..) according to reference manual.
Below is the only information I found in the reference manual about tristate SPI.

According to this information my CFGR1 value is Hex:0x6000001.
lpspi_pin_config_t pinCfg is = LPSPI_SDO_IN_OUT.
lpspi_data_out_config_t dataOutConfig = LPSPI_DATA_OUT_TRISTATE.
bool pcs3and2Enable = true.
Please confirm that configuration and CFGR1 value.
Secondly is there any require HW modification like depicted in the below.

Our schematic design does not have a 10K resistor between MOSI and MISO; instead, it has a 0-ohm resistor. MUST there be a 10K or 1K resistor? Please confirm schematic design.
NOTE: I use S32SDK_S32K1xx_RTM_3.0.0 and S32 Design Studio v2.2
Also I know
"Included on the RTDs comes an example of SPI half duplex transfer. I suggest you take a look at this software supported by S32DS v3.4.Real-Time Drivers for S32K1"