They had controlle of the sky's?

The Luftwaffe never got control of the skies over southern England. One could assert that they denied the use of the Channel to England and that they contested the skies of southern England, but at no point were the Germans winning the Battle of Britain. British production of pilots and planes was able to exceed their losses while German losses in pilots and planes were not equalled by production. The result was that the Luftwaffe slowly lost a battle of attrition over England.

Undertaking an amphibious invasion without air superiority during WWII was incredibly difficult. Without air superiority your (slow, unarmored) transports are vulnerable to enemy interdiction from the air. Given that the German plan for such an invasion included river barges making the Channel passage--not dedicated landing craft and huge numbers of transport ships like the Allies eventually used in 1944--one can see just how vulnerable German transports would be. This is doubly the case because the German navy was dwarfed by the British navy. The Luftwaffe would have had to contest the air to keep the RAF away, support the landings themselves, and keep the Royal Navy from intercepting either the landing force or its supply chain. Paratroopers dropped without support from ground troops can be chewed up fairly quickly--reference later German paratroop assaults on Crete.

Germany certainly wanted the British out of the war, and they would like to have been able to force that effect. However, the Luftwaffe was unable to win the Battle of Britain (which I go into more depth in this post if you're interested), and that effectively removed the possibility of Sea Lion being anything more than a plan on a shelf.

Followup questions from OP and others are always encouraged.