I would like to create a floating action button (to add items to a listview), like google calendar, maintaining compatibility with pre-lollipop Android versions (before 5.0)
There is no longer a need for creating your own FAB nor using a third party library, it was included in AppCompat 22.
https://developer.android.com/reference/android/support/design/widget/FloatingActionButton.html
Just add the new support library called design in in your gradle-file:
compile 'com.android.support:design:22.2.0'
...and you are good to go:
<android.support.design.widget.FloatingActionButton
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="bottom"
android:layout_margin="16dp"
android:clickable="true"
android:src="@drawable/ic_happy_image" />