2 added 181 characters in body
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The triggers literally mean what they say.

When/whenever this/a creature enters the battlefield [...]

... triggers when it enters the battlefield. It wasn't on the battlefield, and then it was. Moving things from the graveyard to the battlefield with Liliana counts.

When/whenever you cast [...]

... triggers when you cast a spell. Moving things around with Liliana doesn't count as casting a spell.

When/whenever you play [...]

... triggers when you play. Playing means casting a spell or playing a land. Moving things around with Liliana doesn't count as playing.

If you haven't controlled a creature since the beginning of your turn, then it has summoning sickness. If Liliana moves a creature from your graveyard to the battlefield, then it hasn't been under your control since the beginning of the turn, and so it has summoning sickness.

The triggers literally mean what they say.

When this/a creature enters the battlefield [...]

... triggers when it enters the battlefield. It wasn't on the battlefield, and then it was. Moving things from the graveyard to the battlefield with Liliana counts.

When you cast [...]

... triggers when you cast. Moving things around with Liliana doesn't count as casting.

If you haven't controlled a creature since the beginning of your turn, then it has summoning sickness. If Liliana moves a creature from your graveyard to the battlefield, then it hasn't been under your control since the beginning of the turn, and so it has summoning sickness.

When/whenever this/a creature enters the battlefield [...]

... triggers when it enters the battlefield. It wasn't on the battlefield, and then it was. Moving things from the graveyard to the battlefield with Liliana counts.

When/whenever you cast [...]

... triggers when you cast a spell. Moving things around with Liliana doesn't count as casting a spell.

When/whenever you play [...]

... triggers when you play. Playing means casting a spell or playing a land. Moving things around with Liliana doesn't count as playing.

If you haven't controlled a creature since the beginning of your turn, then it has summoning sickness. If Liliana moves a creature from your graveyard to the battlefield, then it hasn't been under your control since the beginning of the turn, and so it has summoning sickness.

1
source | link

The triggers literally mean what they say.

When this/a creature enters the battlefield [...]

... triggers when it enters the battlefield. It wasn't on the battlefield, and then it was. Moving things from the graveyard to the battlefield with Liliana counts.

When you cast [...]

... triggers when you cast. Moving things around with Liliana doesn't count as casting.

If you haven't controlled a creature since the beginning of your turn, then it has summoning sickness. If Liliana moves a creature from your graveyard to the battlefield, then it hasn't been under your control since the beginning of the turn, and so it has summoning sickness.