Here is how to root the new BLU Life One, there are probably many ways to do it but this was the best way that I could find.
Note that I tried to root with framaroot, towelroot, and iroot and their apps have failed.
Try this of your own free will, I am not responsible for anything happening to your device (it worked for me so it should work for you).
What you will need:
kingoroot, supersu, busybox, root checker, and titanium backup.
First things first,
Go into settings and check the box next to "Unknown sources".
Next open up the internet tab and search for Kingoroot (kingorootapp dot com)
Click the download button for android (not the windows one)
When it finishes downloading, click in the drop down menu and install the apk.
Open the kingo root app, and click root circle.
After the app is finished rooting your device, you can download Root checker in the play store to ensure that your device is indeed rooted.
Now, I personally don't like kingo root, so the next steps are optional.
In the play store download three apps, SuperSU ( i use chainfire), busybox, and titanium backup (i suggest buying the paid version, it is well worth the money).
Next open up SuperSU (KingoUser should ask to grant SuperSU root access, allow it), and install the SU binary. Do not reboot system.
Next open titanium backup, click the middle tab, then scroll down until you see SuperSU. Long press, and then press install to system apps. (you can do this manually by using ES file explorer and copying the SuperSU.apk file [may need to download it from the internet] in to the/system/app folder.
Now restart your device.
When the device boots back up, check and make sure that your device is still rooted by using root checker again.
If it is still rooted, open SuperSU and make sure you dont have to install the binarys again (you shouldnt have to).
Next uninstall the kingo root app (it will not let you uninstall the kingouser app, for this you must use titanium backup)
Now go into your system, applications and then disable kingouser app.
After doing so, check and see if your device is still rooted (it should be)
If it is still rooted, proceed to use titanium backup to uninstall kingouser app.
Lastly install busy box. If you get an error saying "unable to install choose another location" simply click on where it says "/system/xbin" and change it to "system/bin".
And there you should have a freshly rooted device with no kingoroot. Not saying Kingoroot is bad, i just have always used SuperSU
To the developers of kingoroot, supersu, busybox, root checker, and titanium backup!