A fruit basket contains more apples than lemons. There are more lemons in the basket than there are oranges. The basket contains more apples than oranges. If the first two statements are true, the third statement is

There are fewer oranges than either apples or lemons, so the statement is true.
Easy method: (Try this method to solve without any confusion)
1. A fruit basket contains more apples than lemons = App > Lem
2. There are more lemons in the basket than there are oranges = Lem > Org
Now, Combine the above two results: App > Lem > Org
3. The basket contains more apples than oranges (App > ... > Org) = Yes.
Therefore, the given 3rd statement is true.