No.
Spires Fire during the
Spires Fire step of a player's
Turn, targeting the
Active player's
Units. A
Landmark Minion is not under the
Control of any player so
Spires will never
Attack them. If a
Landmark Minion is under the
Control of a player, it can be attacked by that player's
Spires because it is controlled by the
Active player when the
Spire attacks.