The Spaniard has his own style, nurtured in Barcelona, that he is trying to stamp on Roma, but the start to his reign in the Italian capital has not been plain sailing.
Roma's Luis Enrique is a coach who dares to be different
He need simply look across the Italian capital, at Lazio, where Edy Reja was halfway out of the door after one defeat so far this season before being persuaded to stay.
And as Roma left San Siro after collecting their first point last weekend, Luis Enrique could probably hear the bells tolling for Inter Milan's Gian Piero Gasperini.
The Spaniard's up-and-down start has made tonight's home game with Siena a bit of a judgement day for him, too, though the backing given to Luis Enrique by a new Roma board should probably be taken as earnest.
The intention in appointing a relative novice from abroad was to "do things differently from the past", as Walter Sabatini, Roma's director of sport, put it.
On Luis Enrique, Roma have hung the most fashionable label, advertising the fact that, through nearly a decade as a player and from coaching youths at Camp Nou, he has learnt management at Barcelona, whose style most of Europe swoons over.
There are other aspects of Luis Enrique's background that recommend him.
First, he is tough. Many Italians have a particular memory of Luis Enrique the footballer engraved in their minds: He is in a Spain shirt, blood streaming from his nose during a 1994 World Cup match between Italy and Spain. He had been brutally elbowed in the face by Mauro Tassotti. He played on.
That courage as a footballer was widely admired. Luis Enrique dared cross Spanish football's most perilous frontier, moving from Real Madrid to Barcelona in the late 1990s. He thrived during confrontations between the two.
"He was the best footballer I played alongside," the Brazilian Rivaldo once said, "because of his contagious spirit." His versatility also stood out: Inside-forward, winger, central striker, harrying midfielder, Luis Enrique could do all of them.
The eminent Johan Cruyff was once asked to name his theoretical "World XI" shortly after the turn of the millennium. Cruyff put Luis Enrique at full-back.
Against Inter, Luis Enrique did something similar, by picking Simone Perrotta, a midfielder, and Rodrigo Taddei, a winger, as Roma's full-backs. It was innovative, resourceful. It was not as obviously brave as leaving out the powerful captain, Francesco Totti, as Luis Enrique had in Roma's brief and unsuccessful Europa League campaign, but it showed daring. Luis Enrique has plenty of that.