Learn Italian: Lui si lava con il sapone. - He washes himself with the soap.

si is a reflexive pronoun meaning "himself". In Italian, these pronouns usually go right before the conjugated verb. So, instead of saying "He washes himself", Italian puts it in the order of "He himself washes".

What is the difference between lava and si lava?

lava comes from the normal verb lavare, which just means "to wash" (like washing a car or a shirt). When you add the reflexive pronoun si, it becomes a reflexive action. So, si lava specifically means "he washes himself".

Is the word Lui absolutely necessary in this sentence?

No, you could simply say Si lava con il sapone. In Italian, you can often drop the subject because the verb ending already shows who is doing the action. Including Lui just adds a little extra emphasis.

The word sapone ends in -e. How can we tell if it is masculine or feminine?

Italian nouns ending in -e can be either masculine or feminine. To figure it out, look at the article used right before it! Here we see the masculine singular article il, which proves that sapone is a masculine noun.