Some Uses of "Over" and "Above" as Prepositions

"The birds flew over the lake" is the better sentence because the preposition over is used to say that something is moving across, or from one side to the other, of something else. Above is not used in this way.

The prepositions over and above both tell us where something is in space with respect to something else, but they are not always used in the same way.

Over is used to say that something goes from one side to the other side of something else, or upward and across something. It tells us that something is moving from one place to another.

• The birds flew over [=upward and across] the lake.
• They drove over [=from one side to the other side of] the bridge.
• The boy jumped over [=upward and across] the puddle.
• Our plane just went over [=from one side to the other side of] the Pacific Ocean.

Above is used to say that the position of something is in a higher place than something else.

• They saw a bird on the branch above [=in a higher place than] them.
• Their mother watched them from the window above [=in a higher place than] the yard.
• The birds were flying in circles above the lake. [They were flying in a position higher than the lake, but not moving across it.]

Sometimes over is used to mean above when you are saying that something is in a higher position than something else.

• We hung the picture over/above [=in a higher place than] the desk.
• The light over/above the front porch came on automatically when it got dark.

Above is never used to mean over when you are talking about going from one side to the other side of something. Above is not used to say that something is moving from one place to another.

• They walked above over the bridge.
• The puppy leaped above over the fence and into the neighbor's yard.

When choosing the correct preposition, use over if something is moving across or from one side to the other of something else, and use over or above if something is in a higher place than something else.

I hope this helps.