Rooting the Samsung Galaxy LITE (SGH-T399) I have recently purchased a Samsung Galaxy Lite (SGH-T399). I am having trouble rooting it. It would be easy if I had a Windows PC, but I only have one Mac and one Linux PC. Instructions on how to root the phone would be helpful.
There is really easy ways to root your device from linux/mac using heimdall which is an open source alternative of odin PC.
I will put two methods one auto root ,and an other one to root using heimdall choose the one that suite you best.

First I should say : in my opinion self rooting apps are not really secure ,since you will root blind when you have no custom recovery ,which makes it really hard to get back to a working phone if something goes wrong specially for your device ,like you may noticed on XDA there is a lot of bricked phones without solution. if you still want the auto root follow method 01 ,if you don't method 02 is for you.

Method 1: using impactor (Mac OS and linux)


Get Cydia impactor for your OS Mac OS X , Linux 32bit and
linux 64bit
Depending on you OS for mac OS install the software and run it ,for linux extract the archive somewhere where you have the right to execute then open impactor.
a window like the figure below should appear.


Leave the window open and grab your phone ,GO to settings &gt; developer Options &gt; activate USB debugging also see if there is an option called Verify apps over USB if there is unchecked it.
Now go to settings &gt; security and check unknown source.
Plug the phone to your PC.
On the window of impactor click on start (make sure your phone screen is on it will show an authentication pop-up for adb accept it) and wait if the process succeeded you will be asked to reboot your phone ,if not this method will not work for you go to method 02.




Method 02 : using heimdall on linux (ubuntu and it's variants)

like you said in the question :


  "It would be easy if I had a Windows PC"


We will do the same method but we will use heimdall instead of Odin

Pre-required : : 


Download CWM or TWRP (both odin version choose one of your
liking) and save it on your PC then extract it you will have a file
named recovery.img put it somewhere safe.
Download UPDATE-SuperSU-v2.00.zip and put is on your phone's SDcard we will need it later 


in my example here I will be using ubuntu ,the method remains the same for other ubuntu variants and the same for Mac OS except for the installation part (see method 3 for info).


install heimdall and heimdall-frontend using this command


sudo apt-get install heimdall-flash heimdall-flash-frontend
Once the installation is done launch heimdall-frontend 

sudo heimdall-frontend

This is what heimdall looks like :







Power down your phone then Press and hold Volume down + Home button + power key until the warning screen appears Press Volume Up to go into download mode.
Now Plug your phone to PC.
On heimdall front end go to Utilities tab







click On detect ,you should read device detected on the console at the bottom.





Now that your device is detected we are going to get your current partitions information as a .pit file.
stay on Utilities tab ,click on save as then choose where to put the .pit file once done click on download 







Now switch to Flash tab 





Now click on Browse and choose the Pit file we saved earlier.





Now the Add button (on the right) should be click-able click on it.
click on partition name on the left ,a roll down menu should appear choose recovery.





Click on Browse under the partition ID (not the one under PIT !) then choose recovery.img we extracted earlier.







Now that we are all set , make sure the repartition box is not checked ,that the partition name is set to recovery (look at the above screen-shot) if every thing is right ,click on start at the bottom right.
while heimdall is flashing don't unplug your phone ,don't close heimdall ,don't open other programs ,don't touch the pc or the phone until heimdall show the message flash successful and your phone reboots ,if it doesn't click and hold power button until the phone shut down.
Boot into recovery (power + home + volume up) , (optional : Do a full backup might be handy in case something go wrong) then  flash UPDATE-SuperSU-v2.00.zip we downloaded and putted on your phone earlier.
Now reboot your phone ,you are rooted and have custom recovery installed


Method 03 : On mac OS

replace the first step by this :


Download and install heimdall and heimdall suite ,follow the rest of the steps just like ubuntu method.


References :

heimdall french ubuntu doc (couldn't find english version)

heimdall installation and compilation cyanogenmod wiki

heimdall prebuild downloads on github

heimdall source code