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

Yes

The word "palestra" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only significant difference is in pronunciation. In Brazilian Portuguese, the unstressed vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction; the first "a" and the "e" are often shortened or nearly swallowed, giving the word a more closed, clipped sound. Additionally, the "tr" consonant cluster is typically pronounced with a more dental "t" in Portugal, whereas in many Brazilian dialects, it is more palatalized.

Brazilian Portuguese Examples

1. Eu vou assistir a uma palestra sobre marketing hoje à noite. (I am going to attend a lecture about marketing tonight.)
2. A palestra do convidado foi muito emocionante. (The guest's lecture was very moving.)
3. Eles organizaram uma palestra para todos os funcionários. (They organized a lecture for all employees.)
4. Você anotou as informações principais da palestra? (Did you note down the main information from the lecture?)
5. A palestra será transmitida ao vivo pela internet. (The lecture will be broadcast live on the internet.)

Continental Portuguese Examples

1. Vou à palestra sobre marketing hoje à noite. (I am going to the marketing lecture tonight.)
2. A palestra do convidado foi bastante emocionante. (The guest's lecture was very moving.)
3. Organizaram uma palestra para todos os colaboradores. (They organized a lecture for all employees.)
4. Tomaste nota das informações principais da palestra? (Did you take note of the main information from the lecture?)
5. A palestra será transmitida em direto pela internet. (The lecture will be broadcast live on the internet.)