Resuming on 25-1 on day two, Lancashire batted throughout all three sessions to reach 311-8 at the close of play.
England's Stuart Broad took 3-57, as did fellow paceman Jake Ball.
But 55 from wicketkeeper Alex Davies, 48 from Alviro Petersen and then Livingstone's 63 not out helped the home side end the day on top.
Coming in at number seven, at 156-5, with his side still 86 runs in arrears, Livingstone put on 72 for the sixth wicket with Davies.
And the 22-year-old has so far put on a further 62 for the ninth wicket with Zimbabwean Kyle Jarvis, who ended the day also unbeaten on 36.
Earlier, Warrington-born Steven Mullaney claimed the 50th first-class victim of his career on his old home ground when he had his former Red Rose team-mate, Lancashire captain Steven Croft, caught behind for 15.
Lancashire batsman Liam Livingstone told BBC Manchester:
"I found out I was going to play on Friday afternoon. It's been a very good day for me but also for the team. We're in a strong position.
"There's still two days left in the game so we're looking at building as big a lead as we can, so that we can set attacking fields in their second innings.
"A lot's been said that we've got a young squad but that doesn't mean that we're not talented enough to fill the gap left by Ashwell Prince. We're all working hard to try and prove people wrong."
Notts fast bowler Jackson Bird told BBC Radio Nottingham:
"Obviously, it's a pretty flat wicket but we did well to contain them. After the new ball lost its shine it was tough work.
"It was disappointing we couldn't break that partnership. Once it got soft there wasn't much bounce or movement at all.
"They're only 69 ahead so hopefully we can get these last two wickets early. We can still get a positive result. Hopefully the wicket will start to go up and down and maybe reverse swing will come into it. If we can get a reasonable lead, you never know on day four."

Rory Gallagher's side have recovered from the disappointment of their heavy Ulster semi-final defeat to Tyrone with narrow wins over Longford and Meath.
Galway enter into Round 4A of the qualifier series after surrendering their Connacht title to Roscommon.
Cian Mulligan is the only injury concern for Donegal with a quad strain.
Following their nine point loss to Tyrone in the Ulster championship, Donegal returned to winning ways with a hard-fought victory over Longford and then came out on top of a thrilling shoot-out against Meath earlier this month.
2012 Footballer of the Year Karl Lacey will equal Christy Toye's record of 65 championship appearances for Donegal if he features on Saturday.
Galway had a strong start to their season when they beat Kildare to finish top of Division Two of the National League and earned promotion to Division One for next season.
Kevin McStay's side beat arch-rivals Mayo in their Connacht championship semi-final but they will be disappointed with the way they lost their provincial title after a heavy nine-point loss to Roscommon in the Connacht final.
Lancashire youngster Liam Livingstone marked his first-class debut with an unbeaten half century to build a useful 69-run lead over Nottinghamshire.
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Donegal are hoping the momentum they have gained through the qualifier series can carry them through to the All Ireland quarter-finals.