Here is the official CM11 M9 custom firmware from the team CyanogenMod to update your Samsung Galaxy S4 LTE to the Android 4.4.4 KitKat. Designed by CM, the custom firmware packs quite a ton of features and updates. Here is the complete changelog as posted on the CyanogenMod official website.

CM 11.0 M9 changelog:

* Themes support for additional UI elements
* Heads Up Notifications – Bug Fixes
* Lockscreen – Allow doubletap to sleep when using secure keyguard
* Torch – Improve performance
* Safe Headset Volume – prompt when interfering with 3rd party device (Jawbone, Square, etc)
* Center clock support
* Quick Settings – respect locale changes on additional tiles
* Proximity Wake-Up support – prevent accidental wake-up of device by checking to see if proximity sensor is blocked (eg. Device is in a bag or pocket).
* Spam notification filtering – Set notifications to auto-ignore based on content (perfect for those pesky games that want you to ‘Save 20% on our new game’). Long-press offending notification to set as ignored; manage in Privacy settings.
* Settings Search – Additional improvements and highlighting
* Data Usage Info – Add support for CDMA devices without sim cards
* Bluetooth – Add additional A2DP profiles
* Bluetooth – Disable AVRCP 1.5 by default (fixes various car unit compatibility)
* Email – Fix saving attachments to storage for POP3 accounts
* Translations (Thanks CM Crowdin Team!)
* Account for Play Services induced wake-locks
* Fix encryption on some LG Devices
* Dialer – add support for Korean and Chinese to smart-dialer

- Important: This update is valid for following Samsung Galaxy S4 variants: flteatt, jfltecan, jfltecri, jfltecsp, jfltespr, jfltetmo, jflteusc, jfltevzw, jfltexx, and the International Galaxy S4 I9505 LTE. Follow on to get the instructions about how to update Galaxy S4 LTE to Android 4.4.4 based CM11 M9.

Prerequisites to update Galaxy S4 LTE to Android 4.4.4 CM11 M9:

• Create a backup of all important data in your Galaxy device.
  
• Download and install USB drivers for Samsung Galaxy S4 in your computer.
• Enable USB debugging option by pressing Menu > Settings > Applications. Navigate and tap on Developer Options to ensure that USB Debugging is enabled.
• Make sure that recovery tool like ClockworkMod recovery is installed.
• Ensure that your Samsung Galaxy S4 LTE carries more than 80% of charge. 

How to update update Galaxy S4 LTE to Android 4.4.4 CM11 M9:

Files required: download the CM11 M9 Android 4.4.4 KitKat custom firmware from here;  also download the Google Apps. Save both files on PC.

Here are the steps to update Galaxy S4 LTE to Android 4.4.4 KitKat based CyanogenMod 11 M9:

• Connect your Samsung Galaxy S4 to your computer using USB cable and copy the downloaded files to the SD card of your Galaxy device.
• Disconnect the connection with PC and turn your Galaxy off.
• Boot in to custom recovery mode: press and hold Volume Up, Down and the Power buttons simultaneously until Samsung logo shows up. Leave the keys for half a second and hold again. Use Volume keys to scroll and Power button to select - alternatively you can use Quick Boot app to reboot your Android device in recovery mode.
• Now perform Nandroid backup of your current ROM: select Backup and Restore > Backup. Go back to main recovery menu after backup process is done - very important step to restore back to current OS.
• Data wiping tasks: select wipe data/factory reset > Yes. It will take a few minutes; once done, select wipe cache partition. Next tap on Advance > wipe Dalvik Cache to wipe Dalvik cache data too.
• Select install zip from sdcard followed by choose zip from sdcard. Locate the Android 4.4.4 KitKat based CM11 M9 custom ROM file copied earlier and select it. Tap on yes to confirm installation and wait for the ROM installation to be completed.
• Once installation process is finished successfully, repeat the above step but choose GApps file instead to install the Google apps package on your Galaxy S4 LTE.
• Return to main recovery menu now and select reboot system now to boot up into the latest CM11 M9 custom ROM for Samsung Galaxy S4. It will take a bit of time during the first boot, so kindly be patient.
• Ta da! This was how to update Galaxy S4 to Android 4.4.4 KitKat based CyanogenMod ROM!

How to restore: If you want to return to previous OS on your Galaxy S4 LTE, boot into recovery, select backup and restore then restore your previous ROM by selecting it from the list.