Hi Andrew
Check whether the IRC48 is being halved in SIM_CLKDIV3.
These are the LPUART0 register values when LPUART0 is operating at 115200 Baud from the 48MHz IRC.
#md 40054000 l 8
Memory Display
0x40054000 0f00001a 00100000 00ac0000 00001000 ................
0x40054010 00000000 00000000 00410022 00000100 .........A."....
which look to be what you are also setting.
You can load the binary at http://www.utasker.com/kinetis/FRDM-KL82Z.html to a FRDM-KL82Z board to communicate at 115200 Baud on LPUART0 (OpenSDA VCOM) and either compare its peripheral setups with yours in a debugger or use its memory display menu to browse register setups to find the difference and cause of your issue.
Eg. Here is how I check the LPUART0 registers:
Serial number: 00
Software version V1.4.012
Device identification: KINETIS
Main menu <---- hit enter key to get menu
===================
1 Configure LAN interface
2 Configure serial interface
3 Go to I/O menu
4 Go to administration menu
5 Go to overview/statistics menu
6 Go to USB menu
7 Go to I2C menu
8 Go to utFAT disk interface
9 FTP/TELNET client commands
a CAN commands
help Display menu specific help
quit Leave command mode
3 <--- user 3 and enter to move to the I/O menu
Input/Output menu
===================
up go to main menu
md Memory Display [address] [<l>|<w>|<b>] [num]
mm Memory Modify [address] [<l>|<w>|<b>] [val]
mf Memory Fill [address] [<l>|<w>|<b>] [val] [num]
sd Storage Display {as md}
sm Storage Modify {as mm}
sf Storage Fill {as mf}
se Storage Erase [address] [len-hex]
lp_cnt Read LPTMR CNT
save Save port setting as default
help Display menu specific help
quit Leave command mode
#md 40054000 l 8 <- display 8 long words from address 0x40054000 (address of LPUART0 register block)
Memory Display
0x40054000 0f00001a 00100000 00ac0000 00001000 ................
0x40054010 00000000 00000000 00410022 00000100 .........A."....
Regards
Mark