If you listen closely to the harmonica on Love Me Do, the 2nd half of the melody would suggest he’s playing a chromatic. I imagine that because that melody required notes not so easily available on a diatonic without highly developed bending skills, Lennon will have picked up a chromatic. However, he was first shown how to play harmonica by Delbert McClinton and picked up the basics of note bending from him, so he presumably played diatonic too.