Erik Lamela put the Serie A side ahead after 20 minutes at Washington's RFK Stadium, capitalising on an error by new Blues signing Mark Schwarzer.
But manager Jose Mourinho rang the changes at the break and Lampard - one of six half-time substitutes - drove home a fine equaliser on the hour before Lukaku grabbed a deflected winner a minute from time.
Mourinho's side started brightly, Roma goalkeeper Morgan De Sanctis pulling off a smart stop to deny Michael Essien what would have been a superb breakaway goal with less than two minutes on the clock.
But it was the Eternal City club who opened the scoring - courtesy of a blunder by Schwarzer. The former Fulham goalkeeper failed to deal with Ryan Bertrand's back-pass and left Lamela with a simple tap-in from a yard out after the ball had hit the post.
Schwarzer partially made amends soon after with a sharp save low to his right to keep out a low drive from the lively Pablo Osvaldo.
De Sanctis was again on hand early in the second period, diving to his left to turn away John Terry's powerful header.
The equaliser did arrive just after the hour mark, though, as the much-changed Chelsea line-up picked up the pace. Eden Hazard's slick pass found its way through to Demba Ba and he helped it on towards Lampard, who moved forward and lashed a fierce shot past De Sanctis from 20 yards.
The game was starting to open up, with De Sanctis blocking a Ramires blast and 19-year-old substitute goalkeeper Jamal Blackman called upon to keep out an Osvaldo effort moments later.
Mourinho's frustration was evident on the touchline when penalty claims were waved away after Hazard had been clattered, and further appeals also fell on deaf ears shortly afterwards when Ba too went down in the box.
Source: PA
Source: PA