In an email to Lamont, local branch members said they felt "utterly disillusioned" that their complaints about the trade union Unite were not addressed by the Scottish party and have urged her to speak at a summit today on the fiasco.
The branch also claimed the "inaction" nearly led to "economic catastrophe" through the possible closure of the vital Grangemouth oil refinery.
As revealed by the Sunday Herald, Unite signed up around 100 new members to the local party in a bid to help its favoured candidate, Karie Murphy, secure the candidacy for the Falkirk seat.
Many of the new members had their subscription paid by Unite and were recruited from the Ineos-owned refinery by Stevie Deans, a Unite shop steward at the site and chair of the local Labour party.
However, Unite faced allegations of irregularities during the recruitment drive, including claims that some new members had been signed up without their knowledge.
An investigation by UK Labour led to the constituency party being put into "special measures", while Deans and Murphy were suspended.
The pair were cleared after key evidence was withdrawn, although Labour leader Ed Miliband pointedly refused to offer support to the duo and pushed ahead with reforms to his party's links with the unions.
Emails have since surfaced which appear to show that Unite drafted a "retraction" letter for some of the original witnesses.
The political drama also turned into an economic crisis as Ineos investigated whether Deans worked on the Labour contest with company resources.
The row spiralled into a dispute over the pay and pensions of workers at the plant, which led to Ineos threatening to close the entire plant.
Deans eventually quit his Ineos job 24 hours ahead of the firm announcing the result of its probe.
Lamont has taken second billing to the UK party in dealing with the row, but she has now been thrust into the spotlight.
Ahead of an all-member meeting of the local party today, the Camelon and Falkirk North branch has urged Lamont to attend the summit in person.
The email, sent on Wednesday by a lay official on behalf of the branch, stated: "Many of our local branch members feel that it would be beneficial if you are also in attendance, as a representative of the Scottish Labour Party, to answer our questions."
On the vote-fixing allegations, the official wrote: "Many of our party members feel utterly disillusioned and disappointed that the Scottish party appeared to take no action, despite complaints being made that rules were being broken several months ago."
The official added: "Furthermore, we are aware that complaints were raised that data protection rules were abused, when Labour Party members were contacted by Unite the union, although they were not union members. How did Unite obtain their contacts?"
The email also claimed that the failure to address the allegations led to the Grangemouth crisis: "We believe that the inaction at that time almost caused an unprecedented country wide economic catastrophe and we would be grateful for an opportunity to speak directly to you, as Leader of the Scottish Labour Party."
Branch members are also unhappy that Deans remains as Falkirk West chair: "Finally, a large number of members have indicated disquiet that the meeting may be chaired by Mr Steven Deans, and believe that, if so, it would not be conducive to a completely open and frank meeting where members could express their opinions freely."
The official concluded by informing Lamont that local members were "worthy of your presence".
The Sunday Herald understands Deans will not attend today's meeting.
However, Unite said Deans would continue as chair of Unite in Scotland.
Prime Minister David Cameron waded into the row last week, after he described Deans as a "rogue trade unionist" who nearly brought the Grangemouth plant "to its knees".
Len McCluskey, the general secretary of Unite, described Cameron's remarks as "disgraceful".
Scottish Conservative energy spokesman Murdo Fraser said: "The fact Labour chiefs were warned of this months ago and did nothing is quite incredible.
"Instead of intervening and showing some backbone towards Unite, they cowered away, risking one of Scotland's biggest industries in the process.
"The more details that come out about this shameful saga, the more astonishing Labour's inaction appears."
A SNP spokesperson said: "When her party was in chaos over the Falkirk selection scandal, Johann Lamont was silent and let her London party bosses take charge. If Ms Lamont fails to step up, the question mark over her leadership will continue to grow.
"The focus of SNP ministers has been on saving jobs at Grangemouth. However, there is no question that the inter-relationship between the industrial dispute and Labour's internal politics has been unfortunate and extremely damaging to the workforce."
Sitting Falkirk MP Eric Joyce, whose exit from Labour created the vacancy, said: "Decent Falkirk Labour members want a bit of actual leadership from Johann Lamont. They feel abandoned to Unite. I hope Ms Lamont will attend and insist the fixing inquiry is re-continued."
A Scottish Labour spokesperson said: "The complaints about the Falkirk selection have been fully investigated and acted upon. We are now focussed on ensuring we have a fair and transparent selection and that the local party has a new candidate they can get behind for the 2015 General Election."