Is the word lição the same in Brazilian and European Portuguese?

No.

While the core meaning of "lição" (a lesson or a moral teaching) is identical in both dialects, there is a difference in typical usage regarding schoolwork. In Brazil, "lição" (or "lição de casa") is the standard term for homework. In Portugal, while "lição" refers to the subject matter taught in class, the term "trabalho de casa" (or "TPC") is the natural way to refer to homework assignments. Additionally, there are subtle differences in natural verb usage, such as "revisar" (BR) versus "rever" (PT).

Brazilian Portuguese

1. Eu tenho muita lição de casa para fazer. (I have a lot of homework to do.)
2. A lição de hoje foi muito difícil. (Today's lesson was very difficult.)
3. Ele aprendeu uma lição com esse erro. (He learned a lesson from this mistake.)
4. Vou revisar a lição de matemática. (I am going to review the math lesson.)
5. A professora passou muita lição. (The teacher assigned a lot of homework.)

European Portuguese

1. Eu tenho muito trabalho de casa para fazer. (I have a lot of homework to do.)
2. A lição de hoje foi muito difícil. (Today's lesson was very difficult.)
3. Ele aprendeu uma lição com esse erro. (He learned a lesson from this mistake.)
4. Vou rever a lição de matemática. (I am going to review the math lesson.)
5. A professora passou muito trabalho de casa. (The teacher assigned a lot of homework.)