Can I use Lacerate to choose a unit with 4 might? Just to trigger a chain saying I've chosen this turn? Even if it can't disempower or kill?

Yes, you can. Lacerate's targeting restriction is simply "a unit" — it doesn't care about Might or Empowered status. A 4 Might unit is a perfectly valid target regardless of whether the conditional effects will apply.

Here's why it works:

• Targeting is checked when the spell is finalized (Rule 355.14.b). The "Choose a unit" text means any unit is a legal target. The "if it's [Empowered]" and "if it has 3 [S] or less" are conditional instructions checked on resolution — not targeting restrictions (Rule 355.9).

• When Lacerate resolves against a 4 Might, non-E Empowered unit, both conditions fail: it's not Empowered so no disempower, and its Might is 4 (not 3 or less) so no kill. Instructions that can't be followed are simply ignored (Rule 359.3.e.6). The spell still resolves, it just has no effect.

• This does count as playing a spell and targeting a unit — so it will trigger things like "when you play a spell" or "when you target a unit" abilities.

The only restriction is that you can't choose a target that deterministically results in an illegal action (Rule 355.16) — but nothing here is illegal; the spell resolves normally with no effect on that unit.