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

Yes

The only difference between "lista" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazilian Portuguese, the final "a" is clearly and openly pronounced. In Continental Portuguese, the final "a" is unstressed and undergoes vowel reduction, which makes it sound much more closed, muffled, or nearly silent (similar to the "a" in the English word "about"). The spelling, meaning, and grammar are identical.

Brazilian Portuguese Examples

1. Eu fiz uma lista de compras. (I made a shopping list.)
2. Você viu a minha lista de tarefas? (Did you see my to-do list?)
3. A lista de convidados está enorme. (The guest list is huge.)
4. Ele apagou a lista sem querer. (He deleted the list by accident.)
5. Eu coloquei seu nome na lista. (I put your name on the list.)

Portuguese (Portugal) Examples

1. Fiz uma lista de compras. (I made a shopping list.)
2. Já viste a minha lista de tarefas? (Have you seen my to-do list?)
3. A lista de convidados está enorme. (The guest list is huge.)
4. Ele apagou a lista sem querer. (He deleted the list by accident.)
5. Pus o teu nome na lista. (I put your name on the list.)