Unfortunately, we don't have an example of LIN without the SDK. However, within the cookbook, we have a UART bare-metal example. You can use this project as a base for your own implementation.
Link to the cookbook application note: https://www.nxp.com/docs/en/application-note/AN5413.pdf
Link to the repository of the cookbook: S32K1xx_cookbook - Unnamed repository; edit this file 'description' to name the repository.