The County Championship Division One leaders ended on 273-9 from the day's full allocation of 96 overs.
Tom Smith (70) and Luke Procter (48) shared a second-wicket stand of 84.
But the wily, experienced Tahir, on his home debut, recovered well from being taken for 13 from his first over.
Tahir, who played four matches for Notts last season, all away from home, should have made his first Notts appearance on Friday night in the T20 Blast, but it was washed out.
Nottinghamshire bowling coach Andy Pick told BBC Radio Nottingham:
"We think we've had a good day, especially with them winning the toss and opting to have a bat.
"From 118-1 just after lunch I think we'd have taken the position we are now in.
"Even without Jake Ball, people have stepped up. But, with Stuart and Imran coming into the side, it certainly doesn't make us any weaker!"
Lancashire opener Tom Smith told BBC Radio Manchester:
"You always want a few more but we are happy with where we are.
"There's a bit going on with the new ball, it's been swinging all day."
"Hopefully we can come out and get a few more and get up to 300 for the extra bonus point, then try and make our new ball count."
England fast bowler Stuart Broad took 3-50, backed by 3-78 from South Africa leg-spinner Imran Tahir as Lancashire worked hard for their runs against Nottinghamshire at Trent Bridge.