How to resolve Could not find android.arch.lifecycle:compiler?

Try adding maven { url 'https://maven.google.com' } to your build script repositories:

buildscript {
    ext.kotlin_version = '1.1.50'

    repositories {
        jcenter()
        maven { url 'https://maven.google.com' }
        google()
    }

As a note, you no longer need android.arch.lifecycle:compiler:1.0.0-beta1 if you're using Java 8. You can use android.arch.lifecycle:common-java8:1.0.0-beta1 instead.