Lucivar chose Sutekh for a couple of reasons.
One, he has the option to extract power from another God who doesn't have a bad record against Sunna. It would be foolish for him to solely focus on Loki's power against Sunna, whom history has shown to be exceptional in countering it.
He needed to win—the method, how underhanded it might be, is not a problem.
Second, improving his physical prowess would help immensely in a direct confrontation.
Keeping the stages of the tournament in mind, Lucivar knew that a strong body is the key to his victory.
Because of those reasons, he concluded on choosing Sutekh.
As soon as Lucivar made his choice, agony struck without warning.