If your having trouble doing them together, make sure you have mastered the guitar lick fist. Then, play them together slowly. Don't focus on making sound right, but focus on where the lyrics begin and end in relation to the strumming pattern.
You will find a lot of songs will be syncopated. Or, the lyrics for a verse will start a few seconds before the actual chord change. Try to find where lyrics begin in anticipation of a chord change vs. along with the chord change. Hope this helps!