For logistic regression models in PROC GLIMMIX, you need to use dist=binary link=logit option on the MODEL statement (sorry I missed pointing this out in your program in my previous response). So please add these two options.
For logistic regression models, the estimations are all on the logit scale, so is the LSMEANS statement. To get the lsmeans on the original scale (the probability scale), you can use the ILINK option --
lsmeans &group / ilink ;
For difference in the groups, you use the DIFF option on the LSMEANS statement. The results are also on the logit scale. If you use the OR option, you will get the odds ratios for the group effect --
lsmeans &group /diff or;
Unfortunately, the difference in the probability scale between the groups are not directly available in PROC GLIMMIX. The magnitude of the difference is easy to compute -- you use the results from the ILINK option output, which gives you the estimated probabilities in each group, and compute the difference by hand or by using a data step, however, the appropriate standard errors for these differences are not available in PROC GLIMMIX.