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

Yes

The word "lavar" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. In Continental Portuguese, unstressed vowels (like the first "a" in lavar) are often "reduced" or "closed," making them sound much shorter or closer to a neutral "uh" sound.

Brazilian Portuguese Examples

1. Eu preciso lavar a louça depois do jantar. (I need to wash the dishes after dinner.)
2. Você pode lavar o carro no fim de semana? (Can you wash the car on the weekend?)
3. Ela está lavando as mãos com sabonete. (She is washing her hands with soap.)
4. Vou lavar essa roupa delicada na mão. (I am going to wash this delicate clothing by hand.)
5. É importante lavar bem as frutas. (It is important to wash the fruits well.)

Continental Portuguese Examples

1. Tenho de lavar a loiça depois do jantar. (I have to wash the dishes after dinner.)
2. Podes lavar o carro no fim de semana? (Can you wash the car on the weekend?)
3. Ela está a lavar as mãos com sabonete. (She is washing her hands with soap.)
4. Vou lavar esta roupa delicada à mão. (I am going to wash this delicate clothing by hand.)
5. É importante lavar bem a fruta. (It is important to wash the fruit well.)