Sentinel Sarah Lyons’s second ability only cares if one or more artifacts entered the battlefield under your control this turn. Your creatures won’t get more powerful if more than one artifact entered the battlefield under your control this turn.

The three attacking creatures don’t have to be attacking the same player, planeswalker, or battle.

Once Sentinel Sarah Lyons’s battalion ability has triggered, it doesn’t matter how many creatures are still attacking when that ability resolves. It also doesn’t matter whether or not Sentinel Sarah Lyons is still attacking or on the battlefield.

Sentinel Sarah Lyons doesn’t have to have been on the battlefield at the point in the turn where an artifact entered the battlefield under your control. If an artifact enters the battlefield under your control and then Sentinel Sarah Lyons enters the battlefield under your control later in that turn, creatures you control will still get +2/+2 that turn as long as Sentinel Sarah Lyons remains on the battlefield and under your control.

Use the number of artifacts you control at the time Sentinel Sarah Lyons’s battalion ability resolves to determine how much damage to deal.

Once an artifact enters the battlefield under your control in a given turn, it doesn’t matter what happens to it later. Creatures you control will still get +2/+2 that turn as long as Sentinel Sarah Lyons is on the battlefield under your control.