Lee grabbed his first goals since joining Ipswich from Championship rivals Cardiff earlier this month and Southampton slumped to a sixth defeat in seven league games.
The loss prompted a mass protest against the Saints' supremo Lowe from the majority of the 22,250 crowd.
Supporters angry at the sale of promising youngster Theo Walcott even unfurled a giant banner reading "Lowe Out" in bright red paint.
Southampton head coach George Burley handed Marian Pahars only his second start of the season in place of Walcott following the 16-year-old's record £12 million move to Arsenal.
But it was Dexter Blackstock, another product of club's academy, who had the first chance of the match.
Former Norwich defender Darren Kenton crossed from the right before Blackstock headed goalwards only for up and coming Ipswich goalkeeper Shane Supple to tip the ball round the post.
Kenton came close again from the resulting corner when his close-range strike was cleared off the line by Fabian Wilnis.
Striker Lee fired Ipswich into the lead in the fourth minute.
The former Rotherham and Aston Villa star raced on to Owen Garvan's pin-point centre before holding off a challenge from Darren Powell and picking out the top right-hand corner.
Defender Danny Higginbotham, a former transfer target of Southampton's arch-rivals Portsmouth, had the home side's best effort of an uninspiring first half when he curled just wide with a 40th minute free-kick.
Lee almost doubled the lead in the 68th minute when his fierce right footed shot was saved by the legs of Paul Smith.
But Lee did get his second a minute from time after out-muscling Kenton before unleashing a breathtaking shot into Smith's bottom right-hand corner.
Man of the match Lee almost added to Southampton's misery with a stoppage time header which was saved by Smith.