Yes, you need to get very strong in the overhead press to build big shoulders, but volume and time under tension play a role too. Using lateral raises, add this to your next delt workout. Here's the rep scheme:
25, 15, 10, Rest, 10, 15, 25
Grab a fairly light pair of dumbbells and do 25 reps.
Without rest, grab a slightly heavier pair and do 15 reps.
Without rest, grab yet a heavier set and do 10 reps. If you get a bit sloppy on this last set, no problem. Just don't get so sloppy you look like that guy dancing at a rave who took way too much ecstasy.
Rest for 3 minutes. Now you're going to go back down in weight the same way you came up.
Do 10 reps with the heaviest pair of dumbbells you used previously.
With no rest, do 15 reps with the next lightest dumbbells.
Again with no rest, do 25 reps with the very lightest dumbbells.
The first time you try it you may realize you didn't choose the right weights. No problem, just make a note in your log and choose better next time.