I know they had many casualties in the Battle of Britain, but they had way more planes than they used in this battle. They lacked good boats, but why not think of some other solution?

The Luftwaffe was never able to achieve aerial superiority over southern England during the Battle of Britain, or for that matter at any time at all. Throughout the aforementioned battle, the Germans consistently underestimated the strength of the RAF and British fighter production. This led them to consistently think that they were quite close to finishing the destruction of the RAF. On the other side, the British overestimated German production and consistently thought they were under more pressure than they actually were. In reality, during any given time period the British produced more planes than did the Germans. Also, fighter pilot availability at the end of the battle was greater for the British than it was t the beginning. From the beginning, the Battle of Britain was a battle of attrition, and it was a battle that the Germans were losing.

Without destroying the RAF, an amphibious invasion was a dubious proposition. The German Navy couldn't hope to match the British fleet, and needed the Luftwaffe as a force to try to keep the British Navy out of the Channel. Otherwise, any German transports would be easy prey to British warships. Further, if the Channel was contested then the already difficult logistics of supplying an invasion force across a body of water would become close to impossible. Further still, the lack of suitable landing craft made any invasion unlikely (the Germans proposed using river barges, which would be vulnerable to both weather and enemy fire, as well as being ill suited for the job in other ways).

For any massed airborne invasion, the high costs of the Battle of Crete illustrate how difficult it was for an airborne force to capture an area on their own in WWII. Once on the ground, such forces needed regular ground troops to link up with them in a matter of days to have any chance at success. Undertaking such an invasion in the face of enemy air power would have been even more costly before the troops even got their boots on the ground.

Basically, Operation Sea Lion was never an actionable plan. Without the destruction of the RAF, such an amphibious invasion was not plausible. Further, the Royal Navy provided another obstacle that the Germans had no real answer for. This was illustrated in the 1974 war games which featured British and German officers simulating the invasion. That wargame ended in a clear defeat for the German forces.