The UCL and LSE studies include health and education costs the Lords study you refer to is from 2007, the two identified above are published 2015 and 2016.
The critical bit of this is that as the Lords paper was published 1 April 2008 it would have been based on the data available for the tax years running up to April 1 2007 tax year, which gives very little available data on the impact of immigration from the EU 8 countries.
The studies conducted since by a range of different institutions all confirm that EU immigrants are net contributors, even when taking into account fiscal spending on health and education etc.
On the criticism that was made on the methodology? Well the education costs being put on the British born parent are broadly offset by the fact that the Child benefit and any tax credits are counted as costs for the immigrant when they are household benefits.
Rowthorn too is a difficult one, whilst he discusses the negative impacts of immigration even he agrees that for the UCL study even with a downward revision of the figures based on methodology, EU immigrants have either paid their way or generated a surplus.
Rowthorn is interesting in in his December 2015 study "large scale immigration" because his projections are based on a continued net migration level of 225, 000, now as we know that net migration has been below this point for several years over the last decade, and that the current average is higher because of high net migration in the immediate years after EU8 accession and the slow growth of the EU economy over the last 2-3 years, it is unlikely that this large scale immigration level woud be hit consistently every year for the next 50 years which allows Rowthorn to come to his conclusions.
However, I'm not going to turn this into an academic critique.
The main point is that the most recent data and studies show that immigration, and specifically EU immigration is of net fiscal benefit to the UK.