Meier eventually broke the deadlock just after the half-hour mark with a right-footed shot from the centre of the Dusseldorf box.
Marco Russ and Sebastian Jung had chances to increase Frankfurt's tally during the remaining minutes of the second half, but failed to make the most of them.
Lakic made it 2-0 for the home team just five minutes into the second half when he scored their second goal of the afternoon.
Inui floated in a corner and the forward headed in from the centre of the Dusseldorf box to the bottom-right corner.
Dani Schahin threatened to launch a comeback for the visitors in the 78th minute when he shot home from inside the box, but Meier scored his second goal of the afternoon three minutes from time to wrap up the points for Frankfurt.