Sri Lanka fought back well reaching 140 for one at stumps on day two on Friday.
The Sri Lankans are still 435 runs behind and need a further 235 to avoid follow on.
They lost opener Dimuth Karunaratne for 38 as debutant Chris Jordan claimed a wicket in his first over of Test cricket.
But Kaushal Silva added 82 runs for the second wicket with Kumar Sangakkara as the tourists ended on a positive note after a tough start. Sri Lanka haven't lost a Test Match at Lord's in 23 years.
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Resuming from the overnight score of 344 for five, Root extended the partnership with wicketkeeper Matt Prior to 170 runs, also a record for England against Sri Lanka for the sixth wicket.
The one dimensional Sri Lankan attack struggled on good batting conditions as England scored at a healthy rate on day two.
Seamer Shaminda Eranga threatened to help Sri Lanka regain the initiative when he bowled a good spell in the morning session where he had two wickets in quick succession.