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It was City who dominated the opening exchanges and then came within the width of the post from going ahead when Eliaquim Mangala's volley struck the woodwork on 20 minutes.
The defending champions continued in the same vein and came close again eight minutes later as Edin Dzeko headed a Bacary Sagna cross at Chris Kirkland.
Manuel Pellegrini's side found themselves frustrated in their effort to build on those two openings and Wednesday earned a deserved half-time draw.
First, Dzeko doubled the advantage by sweeping home Jesus Navas's cut-back on 52 minutes, before the Spaniard himself added a third shortly later to effectively end the contest.
Their momentum soon petered out, but there was still time for Dzeko to bag his second as the towering striker completed his brace on 77 minutes, before youngster Jose Angel Pozo got in on the act to add a sixth.
Lampard fired a seventh in the final stages to make it three goals in as many days for him as City cruised into the fourth round.