Ideally they should be used with a mod with quality 17670 or 18650
batteries, or in the smaller sizes like 16340 or 14500 then 'high drain' LiMn/IMR batteries should be used.
The reason for this is that the LR atty's draw a lot of current (in the case of a 1.5ohm atty approx 2.5 amps at 3.7v) and when it comes to high current draw and lithium batteries, then very simply "the bigger the battery the better". A batteries ability to deliver current is given by the "C rating". The "C" stands for capacity. The capacity is the figure all batteries give in mAh.
So to give an example a 2500mAh 18650 battery with a maximum discharge rating of 1C, would be rated to deliver 2500mA (or 2.5 amps). If the 2500mAh battery had a max discharge rating of 2C, then it would be fine to use on current draws up to 5000 mA (5 amps). Higher quality non "high drain" lithium-ion batteries may have maximum discharge rates of 2C. For cheaper cells it is probably best to err on the side of caution.
To give another example, a 600mah CR2, with a max discharge rating of 2C would only be rated to deliver 1200 mA (1.2 amps), which is not enough for an LR atomiser.
Note that in most standard e-cig batteries, the current draw is off the scale for the size of the battery! For example a 180 mah 510 battery is being asked to deliver well over an amp of current with a standard atomiser. This I believe is one of the main reasons why all of these skinny e-cig batteries lose a lot of their "oomph" in a short time, and rapidly lose their capacity. Certainly in my experience they don't usefully last the several hundred discharge cycles that the manufacturers usually claim.
The IMR "high drain" batteries, like those sold under the AW brand, are able to deliver higher current than most lithium-ion batteries (up to 10C in some cases) and so in the smaller sizes these are better suited to this application.
In reality a lot of people use low resistance atty's with eGo's and similar, or in mods they use batteries that are less than ideal. It will work for a while, but at the least it will be likely to reduce the service life of the batteries, and may not give best performance. The potential MOSFET failure is a different issue...
The
MOSFET is part of the power regulation electronics that are on most all mass produced e-cigs (as opposed to mods). My understanding is that they are known to be the cause of early failures on some of them, not because there is anything inherently wrong with MOSFET's, but that the parts used are not a high enough spec for the current pulled by LR atty's. When the MOSFET fails, the lithium cells within the 'battery' are still usable, but the e-cigs electronics won't work any more, so the battery will appear to all intents and purposes to be dead.
Overall my opinion is that you can use LR's on things like the eGo but you should understand that it could result in the battery or MOSFET failing earlier than it would otherwise, and plan accordingly.
