Yep, it's the same lithium. while it's not as reactive as sodium, there's a great deal of chemical similarity.
The fluid in lithium cells is frequently inflammable; lithium has a very high energy density and can release energy quickly if not controlled; lithium batteries have a very specific charging pattern; the battery has a whole is much more vulnerable to heat than nickel-based batteries; and as it discharges it lets off heat. The normal operating conditions aren't unreasonable, but it's not hard to manipulate a Li battery into a state outside them.
For lots of small reasons that taken together, the tolerances for components and manufacturing are not as forgiving, and the overall quality of the battery is caught between the cheapest price and the minimum requirements of the vendor.
One possible failure scenerio is that the battery is cheaply made, and leaks. The ventilation around the battery is adequate but not excessive. The heat from the charging or discharging is enough to ignite the fluid. The heat from the combustion just makes things worse.
Stuff like that.