The latest data are out from the National Science Foundation, showing academic research funding across the USA.  UL's total funded research is ranked third in the state of Louisiana, behind LSU and Tulane.  When adjusted for faculty numbers, however, UL surpasses LSU, and apparently Tulane as well.

The latest data shows that in 2009, UL's research funding was $68M.  The LSU System is the state's research leader with $401M in annual research, with Tulane following at $155M.

UL's research funding is not nearing any foreseeable limit, and in fact appears to be accelerating (dollar amounts in all tables are expressed in thousands):

Year UL R&D Growth
2005 $44,620 --
2006 $47,308 6.0%
2007 $52,075 10.1%
2008 $58,667 12.7%
2009 $68,018 15.9%

LSU System data breaks down research funding per campus, and the Tulane Medical School's research funding last year accounted for $62M, leaving $93M for the main campus.  Using those data, the numbers for all Louisiana research institutions are as follows:

LSU-BR $147,652
Tulane University $92,839
Louisiana $68,018
Tulane Med $62,300
LSU-HSC-NO $58,072
Pennington $42,369
LSU-HSC-S $31,294
UNO $24,783
La Tech $18,060
Southern U $6,865
Xavier $5,690
ULM $4,794
Dillard $4,059
SLU $1,609
Nicholls $1,572
Northwestern St $1,227
McNeese $807
LSU-S $695
Grambling $682
Loyola $662

When accounting for faculty resources, however, it appears that UL has become the research leader in the state.  According to the website CollegePortraits.org, LSU employs 1267 full-time faculty, while UL employs 500.  An accurate breakdown of Tulane's faculty proved difficult.  Tulane lists total full-time faculty at 1100, and Wikipedia reports that the medical school employs 309, leaving 791 for the main campus.

Using these data, it appears that UL has become the most productive research institution in Louisiana:

Institution R&D Faculty $/Faculty
Louisiana $68,018 500 $136.04
Tulane
$92,839 791 $117.37
LSU-BR $147,652 1267 $116.54