You can read the piece, After Defeat, on the Fabian website. Today's Independent carries an extract and a news report.
In part of the piece, Lammy says that Labour has developed a deeply unhealthy party culture which risks "suffocating our party".
The first lesson must be that when parties act undemocratically it comes back to haunt them. This is one of the great lessons of New Labour: a project that hung on to a command-and-control style of politics until the last.
A deal in an Islington restaurant in 1994 led to the creation of two different tribes at the top of the party. It damaged our government and we cannot let it haunt us in opposition. In 1998 the same mistakes were made, this time to prevent Ken Livingstone from becoming the Labour candidate for London mayor. He ran as an independent and won.
In 2007 when the party needed renewing we had a coronation rather than an open debate. I was one of the people who was part of that. I share the blame with the other 300 MPs who made the same decision.
Lammy proposes that Labour's leadership election should give the general public a share of the electoral colleage.
We need to renew our trust in democracy itself. In the leadership election we should introduce a fourth electoral college: the public. One fourth of the votes, alongside members, MPs and Unions, should go to the people who will elect the next government of this country. We should not fear enfranchising them. In the longer-term we need a new democratic culture within our party. We must put the long shadow of the 1980s behind us and give our members a proper voice in their own party. Members should be balloted over policy for our next manifesto, for a start. If we think this is just about leadership, we have big problems.
There is no prospect of the electoral college being reformed for this contest - the time to debate that would make it impossible, though this and other ideas for future reform might be debated by candidates and members.
Other MPs have talked about how to give non-members "a voice if not a vote", though how to do this remains unclear.
A lot of energy will and should go into encouraging people to join Labour and have a vote.
LeftFootForward reports 13,000 people have joined Labour in the last week (or rejoined), though rather overstates the link to The Guardian's report of 100 people leaving the LibDems.
This should go well beyond removing barriers to participation. Of course, using a leadership campaign to recruit and engage depends on the NEC again waiving the party rule (as in 2007) that new members can not participate in elections for six months.
That avoids sending the message "Join Labour today and don't get a say in who our new leader is". (Since the rule is going to be repeatedly dropped, it would make much more sense to now scrap this permanently for national level contests, even if it is viewed as a useful safeguard for constituency elections).
John Healey is promoting the idea of six months free membership for LibDem members who wish to join Labour.
The under 27 introductory rate is £1. This should be extended to all new and former members, as part of a leadership campaign recruitment drive.
[Update: Progress are promoting a petition to the NEC on this point].
But we need to think about engagement as well as recruitment, beyond the induction pack and the hope that local constituency parties will contact new members in their area. There could be lots of small ways to do this:
* Are there ways to mobilise party activists to engage with new members, perhaps adapting the way we use social networks
* Could the party work with its affiliates - like the Fabians, the unions, SERA, CSM and others - who might be able to run events targetted specifically at new party members?
* Why not help all members engage by letting them all know when they join not only about Labour's official affiliate organisations - such the Socialist Societies, but also providing a brief "unofficial fringe" guide the debates in and around the party - from places like LabourList and Left Foot Forward which will help members find their way around the party blogosphere, to pressure groups and campaigns in and around the party?
However, the central point in David Lammy's piece is that Labour is only going to successfully engage new members if it opens up the party culture and organisation in a way which gives greater respect and voice to current members too.