Seven people were detained over the weekend in relation to Lahouaiej-Bouhlel's murderous attack on Nice's Promenade de Anglais on Bastille Day.
One of them, his wife, was released after telling investigators she had little contact with her husband, whom she was in the process of divorcing.
Two others, an Albanian man and woman, are reportedly suspected of providing him with weapons.
Lahouaiej-Bouhlel opened fire on police with an automatic pistol after mowing down 84 people and several imitation guns were found in the lorry's cab after he was killed.
Another detainee was a man believed to have been mentioned as an intermediary in an SMS in which the killer texted "Bring more weapons, take five to C", according to the BFMTV channel.
The fake weapons are one of several elements that puzzle investigators, who have yet to establish any direct links with IS.
The government and the right-wing opposition have been unanimous in declaring the attack "terrorist" and linking it to IS, which claimed the perpetrator as one of its "soldiers" two days after the massacre.
But examinition of Lahouaiej-Bouhlel's mobile phone and computer do not seem to have found signs of contact with Syria, although sources have told the media that visits to jihadi sites replaced visits to pornographic ones recently, according to Nice-Matin newspaper.
The 31-year-old had not been identified as a risk by the intelligence agencies and Interior Minister Bernard Cazeneuve has said that he "seems to have been radicalised very rapidly".
Indeed, neighbours have described a petty criminal who was more interested in salsa and body-building than religion, pointing out that he drank alcohol, did not go to mosque or pray and did not fast during Ramadan.
His relations in Tunisia have also described an emotionally unstable individual with no apparent religious commitment.
His uncle, Abdelfattah, said he was "not normal" and his father, Monthir, told British media that he was "always depressed" when young and had been treated for depression in Switzerland in 2004.
The doctor who treated him, Chemceddine Hamouda, told France's l'Express that he was "violent" and had "problems with his body" but added that the attack must have been the result of radicalisation.
IS incites 'anybody' to violence
Cazeneuve described the Nice slaughter as "a new kind of attack" perpetrated by "people open to [IS's] message, who commit extremely violent acts without being trained".
Lahouaiej-Bouhlel was indeed violent.
He had frequently beaten his wife and hit her mother, according to the wife's lawyer, Jean-Yves Garino, and he received a six-month suspended sentence earlier this year after hurling a wooden pallet at a man in a road-rage incident.
He was known to police for involvement in petty theft, violent and threatening behaviour and vandalism between 2010 and 2016.
On 11 July he rented the truck he was to use in his attack, failing to return it when he should have two days later.
Neighbours say he told his wife "You're going to hear talk of me" and at least one of the individuals being questioned is reported to have said that he had talked of being attracted to radical ideology.
A recent report by the DGSI anti-terror police commented that IS tries to "incite any individual, no matter who" to violent action with the aim of polarising society and forcing Muslims into their camp.
During hearings on last year's Paris attacks, DGSI boss Patrick Calvar warned of a "radicalisation of society", which will lead to confrontation between the ultra-right and the Muslim world", stressing that he meant "not the Islamists but the Muslim world".