Marouane Fellaini headed United in front in the 44th minute after a dominant first-half display, with Paul Pogba going close when he hit the post.
Lukaku nodded in the second from a corner after coming on at half-time and Scott McTominay made it 3-0 in the 70th minute.
Valerenga, who are halfway through their domestic season, created only one clear chance in the second half, with United otherwise untroubled in defence, whether playing with four at the back or three.
Jose Mourinho's side controlled the game and kept possession well throughout as they cruised to a comfortable win.
Henrikh Mkhitaryan saw an early shot saved from inside the box before Pogba shot wide. The France international was the standout player in the opening 45 minutes and struck the post after curling a left-footed shot across goal from 20 yards.
Daley Blind went close when he flicked a cross from Mkhitaryan wide, with United continuing to stretch the play and look for a way past Valerenga's packed defence.
The breakthrough eventually arrived in the 44th minute when Mkhitaryan's cross from the right was headed in by Fellaini, with a deflection sending it past the goalkeeper.
United made nine changes at the break and it was soon 2-0 as Lukaku headed in from a corner.
The lively Anthony Martial then headed over from Timothy Fosu-Mensah's cross before Ghayas Zahid wasted Valerenga's only clear chance when he blazed over from the penalty spot.
United's third goal arrived in the 70th minute as McTominay turned in the box and finished well on the half volley into the far corner.
Lukaku then drilled wide and McTominay saw a shot blocked as United closed out a routine victory.
