The left-hander is unbeaten on 57 at the break, with captain Andrew Gale undefeated on 27.
Earlier this summer, Lyth scored 111 against Hampshire at Headingley, 106 against Somerset at Taunton, and 50 against Durham at Chester-le-Street.
He has been more productive lately in one-day cricket, but the opener has looked in prime form in South London, where he reached his half-century from 70 balls with eight fours.
Lyth has led the Yorkshire reply after the hosts finally dismissed Surrey right on lunch, with just 49.4 overs having been bowled across the first two days due to rain.In much better conditions today, which has mostly been conducted in watery sunshine, Yorkshire lost the wickets of Alex Lees and Jack Leaning in the afternoon session.
Lees had just taken the young left-arm pace bowler Sam Curran for two boundaries in three balls when he fell to the next delivery, somewhat unluckily squeezing the ball on to his stumps to depart for 15.
Curran initially did not realise that the bails had been dislodged and appealed theatrically for lbw until he was made aware of the situation by his team-mates.
Leaning fell for an 11th-ball duck when he chopped on an attempted cut to Stuart Meaker’s first delivery from the Vauxhall End, leaving Yorkshire 47-2 in the 13th over.
Gale, seeking his first fifty in this year’s competition, began impressively as he cover-drove Meaker for four and then tucked him neatly off his pads to the leg-side boundary.
Gale also pushed Tom Curran for a nice four away through backward-point as the third-wicket partnership grew in stature.
Lyth drove with typically flourish through the cover area and took three fours off one Sam Curran over.
At tea, Lyth and Gale have added 60 in 19 overs and the deficit is 160.
The hosts went from 164-5 overnight to 267 all out a couple of minutes after the scheduled end to the session, which had been slightly delayed due to the fact that nine wickets were down.
It was an impressive effort by the visitors to restrict Surrey to only two batting points on a flat surface, after only 49.4 overs had been possible across the first two days.
Yorkshire will now look to go past Surrey’s total in the hope of putting them under pressure on the final day, although the draw at this stage would seem the likeliest result.
In sunny conditions in South London, Steve Patterson struck with the fourth ball of the day to set the tone for the visiting team.
Patterson pounced with his second delivery from the Vauxhall End after Liam Plunkett had completed his unfinished over from the previous day.
Patterson had Ben Foakes caught at second slip by Adam Lyth without addition to the overnight score.
The wicketkeeper was trying to run the ball down to third-man in the type of shot that you often see coaches give as slip-catching practice.
After Foakes’s departure for 14, Steven Davies, who started the day on 29, and Sam Curran fought back well in a resilient stand.
Curran drove Plunkett through the covers for the day’s first boundary, and then he flashed David Willey for four through third-man.
Davies ticked along in sensible style, going on to complete a 69-ball half-century with a four through mid-wicket off spinner Azeem Rafiq.
But Tim Bresnan got rid of him half-an-hour before lunch, Davies trapped lbw playing across his pads for 56 off 98 balls with eight fours.
It concluded a stand of 75 with Curran in 23 overs, and Curran was then joined at the crease by his brother, Tom.
Tom got into his stride with a four through point off Bresnan, shortly before Sam completed his half-century from 82 balls with five fours.
Tom perished for six when he played back to leg-spinner Adil Rashid and was trapped lbw, Rashid striking again four balls later when Gareth Batty was also lbw playing back, the Surrey captain failing to trouble the scorers.
Stuart Meaker was last out when he pushed forward to Rafiq and was caught at slip by Lyth for four.
Sam Curran finished unbeaten on 59 from 98 balls with six fours.