United are severely depleted with up to 10 players missing the trip through injury.
"But sometimes in football, and you have the example with my former club (Man Utd hiring Solskjaer), that sometimes changes on the immediate", he said.
Centre back Chris Smalling picked up his dry cleaning while fellow defender Diogo Dalot, now enjoying a run in the side, went for a fresh trim.
Lukaku had the final say when he made space for himself after collecting Fred's pass and fired home a low right-footed shot in front of the Stretford End.
And while exit from the Champions League looks likely at PSG on Wednesday after the only defeat of Solskjaer's reign in all competitions - 2-0 in the round of 16 first leg back at Old Trafford - fans have been overjoyed with the team's turnaround.
Lukaku cut a relaxed figure on Monday afternoon as he strolled through town in jeans and a khaki bomber jacket.
Palace moved further away from the relegation zone with a 3-1 win at fellow strugglers Burnley thanks to second-half goals from Michy Batshuayi and Wilfried Zaha.
"We're playing against one of the best teams in Europe with some absolute quality players but who knows?"
Solskjaer's side remain unbeaten domestically since he replaced Jose Mourinho, with United moving above Arsenal into fourth place. United will play a minimum of 11 more matches this season and Sanchez now stands to miss nine of them, starting with Wednesday's Champions League Round of 16, second leg tie away to Paris St-Germain.
"It's incredible. You feel a lot of emotions and I'm very happy and hopefully there will be many more to come". They're confident going into the game, even knowing we're 2-0 down. I just want to do all I can on the pitch.
"But what for me is the most important thing is next time we have a penalty he goes again".
United's 89th minute victor in their 3-2 victory against Southampton this weekend was just the latest indicator that the good times are back at Old Trafford.
But in the months since, United's dramatic upturn in form has seen them climb back into the top four, giving themselves a real chance of salvaging something from a season that had threatened to go completely off the rails before the turn of the year.