Try changing your baud rate. To get the 13 dominate bits that you need for LIN, you can shrink your baud rate proportionally. For example, if your baud rate is 19200, your standard bit time is ~52us/bit. A normal transfer w/ data byte value of '\0', will have 9 bit times of the dominant value (start bit + 8 data bits), which is ~470us of total dominant time. You need to have 13 bit times, which would be ~677us of dominant time. If you do the inverse math, which means, which baud rate do I need so that a normal 9-bit times would use 677us of dominant time, you would find out that a baud rate of ~13,292 would be sufficient. You can validate this with a scope to determine if your times are long enough.
Simplified math to increase the baud rate the time (what normally takes 13 bit times, you want to do in 9 bit times):
baudrate 9
------------- * ---------
13
Does this make sense?
