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

Yes

The meaning, spelling, and grammatical function of "lugar" are identical in both Brazilian and Continental Portuguese. The differences are strictly phonetic:

• Pronunciation (Brazil): Vowels are generally more open and clearly articulated. The final "r" is often pronounced as a strong, aspirated sound (similar to the "h" in "house") or a retroflex "r" depending on the region.
• Pronunciation (Portugal): Vowels are more closed and frequently undergo "vowel reduction," where unstressed vowels are shortened or nearly swallowed. The final "r" is much more subtle, often being a soft uvular sound or almost silent.

Brazilian Portuguese Examples

1. Este é o meu lugar favorito. (This is my favorite place.)
2. Não tem mais lugar no carro. (There is no more room in the car.)
3. Você sabe o lugar onde nos encontramos? (Do you know the place where we meet?)
4. Coloque as chaves em um lugar seguro. (Put the keys in a safe place.)
5. Aquele lugar é muito legal. (That place is very cool.)

Continental Portuguese Examples

1. Este é o meu lugar preferido. (This is my favorite place.)
2. Não há lugar no autocarro. (There is no room on the bus.)
3. Sabes o lugar onde nos encontramos? (Do you know the place where we meet?)
4. Põe as chaves num lugar seguro. (Put the keys in a safe place.)
5. Aquele lugar é muito giro. (That place is very nice.)