Is lithium grease suitable for lubricating the steel headset cups when pressing them into the aluminium frame?
Yes, totally suitable. Of all the remotely common grease types, there's not really a scenario on bikes where the type matters for this application unless it's a titanium or stainless frame, and then use anti-seize.
As someone who presses things into bike frames on a regular basis and lives/works in a rainy climate, I do always use grease, but it's primarily for information, not corrosion resistance. Greasing the surface every time comes close to normalizing the contribution that surface friction makes to the force required, so problems with the press fit are easier to pick out in both the too loose or too tight direction.