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

Yes.

The word "lavei" is the first-person singular of the verb lavar (to wash) in the pretérito perfeito do indicativo (simple past). There are no differences in meaning, grammar, or spelling between Brazilian and Continental Portuguese. The only difference is in pronunciation:

• Brazilian Portuguese features more open vowels and a more "syllable-timed" rhythm, where each syllable receives a more distinct weight.
• Continental Portuguese features more closed or reduced vowels and a "stress-timed" rhythm, where unstressed syllables are much shorter or nearly swallowed.

Brazilian Portuguese Examples:

1. Lavei a louça depois do jantar. (I washed the dishes after dinner.)
2. Lavei meu carro hoje de manhã. (I washed my car this morning.)
3. Lavei a roupa suja. (I washed the dirty clothes.)
4. Lavei o rosto com água gelada. (I washed my face with ice-cold water.)
5. Lavei as frutas antes de comer. (I washed the fruits before eating.)

Continental Portuguese Examples:

1. Lavei a loiça depois do jantar. (I washed the dishes after dinner.)
2. Lavei o carro hoje de manhã. (I washed the car this morning.)
3. Lavei a roupa suja. (I washed the dirty clothes.)
4. Lavei o rosto com água fresca. (I washed my face with fresh water.)
5. Lavei as frutas antes de as comer. (I washed the fruits before eating them.)