Ok, the file you have there ending in _HOME.tar.md5 contains the full firmware upgrade including bootloader (mbn files), baseband (modem), ROM (system, kernel, and recovery), and CSC (written to cache for recovery to apply to system and give you proper carrier apps and access point names for data/phone operation). If you want everything in one go, including the bootloader upgrade, you may want to backup everything from your phone's internal storage first. I'm not sure you would want to use mobile Odin for an entire firmware upgrade operation, and you'd especially want to have an actual desktop Odin available in case anything goes wrong to recover. (it's also not recommended by Chainfire to use on LP yet)
Odin 3.09 for Windows
New: Cold boot your phone into Odin by removing your battery and USB cable, then waiting 5 seconds, reinsert your battery and do VolDown + Home + Power to boot directly into Odin from OFF. Once Odin is started, you can insert your USB cable. Some people have had issues where bootloader and/or modem wouldn't upgrade without a cold boot.
This *should* be sufficient to upgrade fully to DOC4:
then press Start. It would likely upgrade the bootloader even without the "Phone Bootloader Update" box checked
Once it's finished, it will reboot your phone and start installing the CSC. I would recommend going back into recovery after that completes by using VolUp+Home+Power buttons, then using wipe data/factory reset. I don't think it's entirely necessary, but it should save you from any issues caused by previous settings on KK firmware.
Once you boot up, go through the wizard until you reach your home screen. Open up the dialer and call *#1234# - this will open up a version info dialog, telling you which version your ROM (AP), baseband (CP), and carrier data (CSC) are. Make sure they're all ending in DOC4! If they aren't, get back to me. If you want to check your bootloader version as well, get Phone INFO Samsung from Google Play and go to the firmware tab in it. I don't know how to check it from dialer. I am fairly sure the DOC4 bootloader can be downgraded (it's a Canadian tradition) although it WILL trip Knox on downgrade (do any carriers here actually care?) so I wouldn't be afraid to use it.
IF you want to upgrade and be sure that the bootloader is not included in the upgrade, you will need the tools to create Odin flashable firmware files.
DISCLAIMER: I have no clue if LP will run on KK bootloader, you would have to confirm!
img2tar.7z
Extract that and you will find the folder img2tar, inside of it are a bunch of folders that you can fill up with files extracted from the _HOME.tar.md5 (using 7-zip). I've placed empty files in ap, bl, csc, and cp folders to tell you which file goes where. All you have to do after placing them is run the .bat files to generate the tar.md5's.
If you wish to forgo the bootloader, don't use make-bl.bat.
When using Odin with these generated tar.md5's, this is how you will fill it out before pressing Start:
I still recommend doing a factory reset via STOCK recovery with both methods.
Once you've confirmed everything seems ok, you can install TWRP easily from Odin using only the AP box with
this TWRP recovery flashable tar.
Rooting can easily be done by putting
recovery flashable zip latest SuperSU on your internal storage or sdcard, then flashing that from TWRP.
Issues I've run into while firmware upgrading:
Modem doesn't upgrade - reflash CP file from last step only. If that doesn't work, reflash both CP and BL (modem might require new bootloader).
Modem & bootloader don't upgrade - COLD BOOT: remove all power from phone (unplug, remove battery) then reinsert battery and do volDown+Home+Power to get into Odin, then insert USB cable.
Infinite length loading screen, never boots - data partition is blank or incompatible with ROM, boot into STOCK recovery and wipe data/factory reset to fix. (if you used NAND Erase All in Odin this will happen)
T-mobile boot logo - CSC flash failed (you have no carrier data), reinstall stock recovery and carrier data by reflashing AP and CSC through Odin.
Phone doesn't show up in Odin COMs - No Samsung drivers installed -
download them here.
EMERGENCY RE-PARTITION FILE - DO NOT USE THIS unless you are somehow bricked but still able to access Odin through VolDown+Home+Power. Use in Odin with _HOME.tar.md5 in AP slot, Re-Partition, PIT file in slot.