Although a creature put onto the battlefield this way is attacking, it was never declared as an attacking creature. Abilities that trigger whenever a creature attacks won't trigger when that creature enters attacking.

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Leonardo's last ability will trigger twice. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, planeswalkers, and/or battles at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.

If Leonardo is dealt lethal damage at the same time that you gain life, he won't receive a counter from his last ability in time to save him.

If a creature spell's sneak cost was paid, the creature it becomes enters tapped and attacking the same player, planeswalker, or battle as the creature that was returned to its owner's hand to pay its sneak cost. This is a rule specific to sneak; in other cases, when a creature is put onto the battlefield attacking, that creature's controller chooses which player, planeswalker, or battle it's attacking.

If you gain an amount of life "for each" of something or "equal to the number" of something, that life is gained as one event and Leonardo's last ability triggers only once.

In a Two-Headed Giant game, life gained by your teammate won't cause Leonardo's last ability to trigger, even though it caused your team's life total to increase.

Leonardo's last ability triggers just once for each life-gaining event, whether it's 1 life from Illegitimate Business or 3 life from Guac & Marshmallow Pizza.

Spells can only be cast for their sneak costs any time you could play an instant during the declare blockers step on your turn (after your opponent has decided whether to block).