Google has updated Android System Webview for Lollipop, but is only exclusive for stock Nexus ROMs. The app is available in Play Store but renders unusable for non-Nexus ROMs. The 'framework-res.apk' contains a string that links the webview to the stock package 'com.android.webview,' and the updated webview uses the package name 'com.google.android.webview.' This mod replaces the link for the Webview from stock to the updated package.
An Xposed module is available but Xposed Framework is in its 'Super Alpha' stage for Android 5.1.1. This mod is for those who don't want to test an unstable build yet.
NOTE: Ensure that a backup is available in case things get out of hand.