The term 'give a lift to' can be expressed in two different ways in a crossword puzzle: ELATE (5 letters) and ELEVATE (7 letters). ELATE means to make someone very happy or cheerful, while ELEVATE means to raise or lift up. Both terms imply helping someone to feel better or to reach a higher level. In this context, the phrase 'give a lift to' could refer to providing emotional support or encouragement, or it could mean providing physical assistance to help someone reach a higher level.