Someone who is alive has not died and their life continues. You use alive after a link verb like ‘be’ or occasionally after a noun. You do not use ‘alive’ in front of a noun.

1. She didn’t say whether he was still alive.
2. I am the happiest man alive.

A living person, animal, or plant has life and is different from someone who is dead or something that does not have life.

3. …or see living artists at their work.
4. Baboons, even the smaller living species, are very formidable creatures.

Someone who is lively is active and enthusiastic. Behaviour and activities can also be described as lively.

5. Before her marriage she had been lively and alert and carefree. 6. The debate promises to be lively.