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

No

While the grammatical meaning of "lhe" (the third-person indirect object pronoun) remains the same in both dialects, there are significant differences in typical usage and syntax (placement).

• Typical Usage: In Brazil, "lhe" is often reserved for formal writing or professional speech. In casual, everyday Brazilian Portuguese, people frequently substitute "lhe" with "te" (even when referring to você) or use prepositional phrases like "para ele" or "para ela." In Portugal, "lhe" remains the standard, essential indirect object pronoun for the third person (ele, ela, or você) in both formal and informal contexts.
• Syntax (Placement): Brazilians predominantly use proclisis (placing the pronoun before the verb), such as "Eu lhe disse." In Portugal, the standard is enclisis (placing the pronoun after the verb), such as "Eu disse-lhe."

Brazilian Portuguese (Natural formal/professional usage)

1. Eu lhe entreguei o relatório. (I delivered the report to him/her/you.)
2. O professor lhe explicou a matéria. (The professor explained the subject to him/her/use.)
3. Ele lhe enviou um e-mail. (He sent him/her/you an email.)
4. O cliente lhe pediu um desconto. (The client asked him/her/you for a discount.)
5. Ela lhe disse a verdade. (She told him/her/you the truth.)

European Portuguese (Natural standard usage)

1. Eu entreguei-lhe o relatório. (I delivered the report to him/her/you.)
2. O professor explicou-lhe a matéria. (The professor explained the subject to him/her/you.)
3. Ele enviou-lhe um e-mail. (He sent him/her/you an email.)
4. O cliente pediu-lhe um desconto. (The client asked him/her/you for a discount.)
5. Ela disse-lhe a verdade. (She told him/her/you the truth.)