At tea, Australia were 191 for one, with Rogers 81 not out and Steven Smith -- dropped on 50 -- 62 not out.
The pair had so far added an unbroken 113 for the second wicket.
Left-hander Rogers -- who plans to retire after this series -- knows 'the home of cricket' well from his time with Lord's-based county side Middlesex.
This was the 37-year-old's seventh fifty in eight Test innings although none of those knocks had yet led to a century.
The only setback so far for the Ashes holders, looking to level the five-match series at 1-1 after England's 169-run win in the first Test in Cardiff last week, was the loss of David Warner for a well-made 38 before lunch.
Australia captain Michael Clarke won the toss and elected to bat first on what looked another typically good Lord's pitch.
Initially overcast skies offered a hint of swing movement but long before tea the sun had broken through as conditions for batting eased.
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