From our experience with our IPA on a combi-vessel system, we've found LG-ratio impacts both mash efficiency and lautering performance (differential pressure during collection). In both cases, however, it hasn't had an impact on its own (p = 0.963 and p = 0.651, respectively), but rather in conjunction with other factors.
With mash efficiency, the impact of LG-ratio is significant in interactions with vorlauf time fraction (fraction of conversion+vorlauf time) (p = 0.002), diastatic power of the base malt lot (p = 0.0163), and to a much lesser extent, lower mill gap setting (p = 0.276). With lautering performance - which among others things we define as the mean dP throughout collection - the impact of LG-ratio is significant in interaction with total mash time (p = 0.029).
Below are some graphs of the models - note that our LG-ratio is in qt/lb, so roughly double that to get the w/w ratio.
Also, a key:

This model graph suggests that mash efficiency in thicker mashes (lower ratios) benefit from longer vorlauf times (relative to conversion time, so for example, if your total mash time is 60 minutes, a vorlauf fraction of 0.75 would be a 15 minute conversion and 45 minute vorlauf). And vice versa - mash efficiency in thinner mashes tends to benefit from shorter relative vorlauf times (using the 60 minute total mash time again, this would be a 54 minute conversion time and 6 minute vorlauf). I have no idea why this would be, but the anonymous post above may be on to something.
Below is the model showing impact of LG-ratio interacting with diastatic power. It suggests thicker mashes can minimize the impact of diastatic power, but if you have a good diastatic power, you may really be able to bump your mash efficiency by using a thinner mash.
The lower mill gap setting graph isn't as cool (hence the higher p-value), but a smaller lower mill gap seems to help mash efficiency in thicker mashes. This tends to be the case with finer grist, but careful with fine grist in thick mashes. Lautering performance will more than likely be affected.
A quick note about the dP model: it's not the most reliable at predicting due to the data coming from production runs. In other words, the higher dP runs are interfered with (of course), so the actual numbers are artificially low. But we do think the general relationships remain intact.
Anyway, for lower dP in thicker mashes, the model suggests longer total mash times (regardless of vorlauf fraction). It seems to care less about total mash time as the mash gets thinner (for lautering performance - not necessarily mash efficiency).
And one final disclaimer: this is for one brand in our production brewhouse. Your mileage may vary.
Hope this helps, cheers!
------------------------------
Trent Leslie
MadTree Brewing Company
Cincinnati OH
(419) 651-5914
------------------------------