The original report was published in July 2014, with parks consultant Peter Neal as lead author. It set out the funding position for public parks in the UK and issued calls to action to prevent parks declining further.
It has been widely read and used to argue the case for parks and is still frequently cited in the national press, more than 18 months after being published.
The second report will compare the state of parks funding today to two years ago, including case studies of parks that have improved or declined, and will report on progress made as well as suggesting new courses of action.
In the tender documents HLF outlines possible differences in the new report - including simpler survey questions and the hope that local authorities may be more vocal this time around.
"During research for the first report many local authorities were anxious not to be named or shamed but we believe some are now past that point and keen to explain why parks may be suffering and the difficult funding choices they are being forced to make."
HLF explains: "The aim of this research must be to update on progress, or regression, since the last study but we are keen this report is more illustrative of what is actually happening on the ground, what changes are happening (both positive and negative), where tensions lie between management/funding/use, and how changes are particularly impacting upon people and local communities.
"Evidence for the latter may be more difficult to obtain but we are keen to explore what might be possible maybe focusing on particular geographic areas or local authorities."
As with the 2014 version, the research project will require the production of an indepth report and a shorter, "punchier" report which can be used for advocacy purposes.
The contract is worth £50,000. HLF expects research to begin 26 February with the final report to be submitted by 8 July. The contract will be let by the National Heritage Memorial Fund.
Applications must be submitted by noon on 12 February to Drew Bennellick at firstname.lastname@example.org. See the Government contracts website for full details.