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

Yes

The spelling, meaning, and grammar of "lápis" are identical in both Brazilian and Continental Portuguese. It is a masculine noun that remains invariant in the plural (the word does not change, only the article: o lápis / os lápis). The only difference is in pronunciation:

• Spelling: Identical.
• Meaning: Identical (pencil).
• Pronunciation: In Continental Portuguese, the final "s" is almost always pronounced as a "sh" sound ([ʃ]), and the vowels are more closed. In Brazilian Portuguese, the pronunciation of the final "s" varies by region (it is often an [s] sound in São Paulo or a [ʃ] sound in Rio de Janeiro), and the vowels are generally more open.

Brazilian Portuguese Examples

1. Eu esqueci meu lápis na escola. (I forgot my pencil at school.)
2. Você pode me emprestar um lápis? (Can you lend me a pencil?)
3. O lápis de cor quebrou. (The colored pencil broke.)
4. Eu preciso de um lápis grafite para o desenho. (I need a graphite pencil for the drawing.)
5. Guarda os lápis no estojo, por favor. (Put the pencils in the pencil case, please.)

Continental Portuguese Examples

1. Deixei o meu lápis na escola. (I left my pencil at school.)
2. Podes emprestar-me um lápis? (Can you lend me a pencil?)
3. O lápis de cor perdeu-se. (The colored pencil was lost.)
4. O lápis está em cima da secretária. (The pencil is on top of the desk.)
5. Escrevi a morada com o lápis. (I wrote the address with the pencil.)