You can not *safely* use the EO-9 with RCR123 size 3.7V Li-Ion cells. Lithium Cobalt oxide is, in 99% of cases, rated for a maximum discharge rate of 1.5-2C, or in the case of a ~500-600mAH cell, ~0.9A-1.2A is the maximum safe continuous drain rate. The EO-9 would be at least a 4C discharge rate, double the rated maximum. The HO-9 is actually close to a 3C discharge rate, however, provided you use it in short bursts the HO-9 will work pretty well, just keep a close eye on the cells and test frequently for signs of aging.
The difference between a 3.6V and 3.7V rated Li-Ion cell is simply old vs new labeling. Li-Ion used to be considered 3.6V nominal, charged to 4.1V, nowadays the design has been tweaked to handle being charged to 4.2V, so they changed the label voltage to 3.7V. It is very unlikely that you could buy a new Li-Ion cell that is actually based on the older designs that could only be charged to 4.1V, so what is likely, is that you simply bought cells from company that has "moved forward" with the labeling used by the industry. Many companies are simply still calling them 3.6V cells, it really doesn't make much difference, the important thing is that you get quality cells that can handle the current, but no matter what cells you buy, you are going to be way over the rated maximum discharge rate on those lamps.
They are very likely to fry any lamp intended to be used with primary CR123s as they have substantially higher working voltage.
You are not going to get "320 and 380" lumens out of a pair of Li-Ion cells that are less than half the minimum ideal size to drive those lamps. Run them on a pair of 17500s as bare minimum and you should have much better results. Also remember that those are bulb lumens at the voltage listed in the specifications charts, you have to take into consideration losses from reflector, lens, etc. Fresh off the charger, a pair of 17500s will drive an EO-9 to around 250 torch lumens. Also remember that Torch Lumens and SureFire Lumens are very different things. Surefire is de-rated even further.