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

Yes

The word "lá" is identical in both Brazilian and Continental Portuguese regarding its meaning (an adverb of place indicating distance from both the speaker and the listener), its grammatical category, and its spelling. The only differences between the two dialects are phonetic, specifically involving the phonetic realization of the vowel and the prosody (the rhythm and stress) of the sentence.

Brazilian Portuguese Examples

1. Eu deixei meu celular lá na mesa. (I left my cell phone there on the table.)
2. Vamos lá, você consegue! (Let's go, you can do it!)
3. Ele mora lá no Rio de Janeiro. (He lives there in Rio de Janeiro.)
4. Lá se vai o meu dinheiro com esse ônibus. (There goes my money with this bus.)
5. Deixa tudo lá, não se preocupe. (Leave everything there, don't worry.)

European Portuguese Examples

1. Eu deixei o meu telemóvel lá na mesa. (I left my mobile phone there on the table.)
2. Vamos lá, tu consegues! (Let's go, you can do it!)
3. Ele vive lá no Rio de Janeiro. (He lives there in Rio de Janeiro.)
4. Lá se vai o meu dinheiro com este autocarro. (There goes my money with this bus.)
5. Deixa tudo lá, não te preocupes. (Leave everything there, don't worry.)