OK, here it is. I finally made to Root my Samsung Galaxy S4 I9505 also known as LTE.
I wrote about rooting this phone before, and that was just a try – unfortunately I could not root it that way.
This time I made it and this is how it goes:
To root your Samsung Galaxy S4 I9505 (applies only for this model) you need to download CF-Auto-Root-jflte-jfltexx-gti9505.zip file and to unzip it on your PC. Also, you need ODIN (I use ODIN 3.07), and Samsung S4 I9505 with a battery level at 80% at least.
Unzip your CF-Auto-Root-jflte-jfltexx-gti9505.zip file inside director where you keep ODIN. Power OFF your Galaxy S4 LTE and boot it into Download mode. To do that press and hold Volume Down + Home + Power buttons all together until you see Android Green Robot. Release buttons and then navigate to the Download by pressing Volume Up.
Now, Run ODIN on your PC (if using Vista or Windows 7 then Run As Administrator).
Connect your phone with PC using USB cable. Wait until ODIN recognizes your phone.
Now in ODIN choose file you want to write on your phone – CF-Auto-Root-jflte-jfltexx-gti9505 but before that make sure that Auto Reboot and F. Reset Time options are selected, and Re-Partition is not selected. This is important, so be careful.
When you have done all now just hit Start in ODIN.
Wait till installation process is completed. Your phone will reboot and when this root process is finished PASS message will appear on the left in ODIN.
Now you have rooted your Samsung Galaxy S4 I9505 with Lollipop installed.