If my Lucian moves into an uncontrolled battlefield with an equipment equipped, does he still get the +1 from Assault?
No, your Lucian will not gain the +1 Might from Assault when moving into an uncontrolled (empty) battlefield.
According to Rule 733.1.c, Assault is functionally short for "While I am an attacker, I have +X [M]." As established in RiftJudge FAQ #863 and #1818, moving a unit into an unoccupied battlefield initiates a non-combat showdown, not a combat. Because there is no opposing unit present to defend, your unit does not receive the "Attacker" designation.
Key points:
- Assault is a passive ability that is only active when a unit has the "Attacker" designation.
- The "Attacker" designation is only assigned during a combat showdown, which requires an opposing unit to be present at the battlefield.
- Moving to an empty battlefield results in a non-combat showdown, meaning your unit does not become an attacker and the Assault bonus does not apply.
If an opposing unit were to move to that same battlefield later in the same turn, a combat showdown would then begin, at which point your Lucian would gain the Attacker designation and the Assault bonus would activate.