Hi-
There a some references on the effect of pressure on the lean flammability limit.
Here's what [1] says:
For a methane-air mixture, the percent of methane limits are 6.0 and 17.1 at 10 atmospheres.
At 125 atmospheres, the limits are 5.7 and 45.5 percent methane.
There are some other references. Burgess and Hertzberg wrote a paper in 1975 on the effect of pressure on the lean flammbility limit (LFL). I cannot find my copy of the paper so I can't give you a title. But Burgess & Hertzberg indicate that for methane, the LFL remains constant up to 100 atmospheres. For natural gas, the LFL goes from 5 % at 100 atm to 2 % at 700 atm.
I have another reference regarding the effect of pressure on the lean limit for natural gas (Wierzba and Karim, 1990) if you are interested.
Also, there is a 1997 paper by Yamamoto that says pressure has little effect up to pressures of about 41 atmospheres.
1. Rose, J.W., and J.R. Cooper (editors). "Technical Data on Fuel", Seventh Edition, A Halsted Press Book printed by John Wiley & Sons, New York, New York, 1977. See Table 5.3, which is called "Effect of Pressure on Inflammability Limits". There are also a couple plots related to the effect of pressure.
Hope that this helps.