After the hosts declared at 562-7 on day two, they bowled Yorkshire out for 311 early on the final day despite Lyth’s ton, before enforcing the follow-on.
And at 88-5 with 19 overs remaining, appeared in with a sniff of victory.
However, they ran out of time as Yorkshire middle and lower order chewed up enough balls to see out the remaining overs and finish 141-6.
Lyth was delighted with his century and admitted Taunton is a ground he loves playing at.
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“It’s different to up North. I love batting down here, it’s a good batting wicket,” said the Whitby man.
“I think that’s my 800th run down here in seven games. It’s pretty flat and if you get past the new ball it doesn’t do much so it was nice to cash in, but it was unfortunate to go out the way I did (caught, first slip).”
Lyth could only make 18 in the second innings as he fell victim to a peach of a delivery from Jamie Overton, and he has had an inconsistent start to the season
He said: “Especially at Headingley it’s been tough, but I played a good knock against Hampshire in the first game at home, (111) which was pleasing.
“I’ve had a couple of bad decisions, but that can happen.
“I’m hitting the ball really well, and happy with how it’s going so far.”
Lyth expects to be back to his consistent best soon.
“Everything’s in order, so pretty close,” he added.
“I guess I’ll answer that question later on in the summer but at the moment it’s going pretty well.”
Yorkshire now sit second in the Specsavers County Championship division one table after one win and four draws in five matches.