You raise a good point. Upon further study, it does appear that the "man's heart" was given to the eagle, not the lion, based on the context and flow of Daniel 7:4. Here are the key points:
1) The verse is describing the first beast, which has the body of a lion with eagle's wings. This clearly represents Britain, with its naval power symbolized by the wings.
2) It says "the wings thereof were plucked." This refers to Britain losing its colonies, represented by the wings/eagle's wings being plucked.
3) It then says "and it was lifted up from the earth and made to stand upon the feet as a man