#3 He was not yet cut out for the job
Real Madrid is the biggest club in the world, possessing a plethora of world-class players and an illustrious history, and as such, the club is expected to win every match and every trophy it contests in.
This puts any incoming manager under enormous pressure to succeed instantly, as the instant success syndrome is so ingrained in the club that neither players nor coaches are given the requisite adaptation stage as obtainable at other clubs.
Real Madrid is a big club, and the huge egos present at the club requires marquee managers to coach them, but sometimes even some of the greatest of them all struggle to cope with the demands of the club, evidenced by Mourinho and Ancelotti's travails.
As stated earlier, Lopetegui has had a moderate coaching career till date, and doesn't have the requisite CV to survive as Real Madrid coach, and more often than not, coaches with such sparse achievements fail to cut the grade at the Bernabeu, although Zinedine Zidane is a notable example (though his familiarity with the club as a result of his legendary playing career gave him an edge).
Only the biggest coaches can survive a failure at Real with their reputations still intact, with Mou and Ancelotti as examples who went on to other big jobs despite getting the sack at Real Madrid.