Lithium Ion batteries have NO business inside any aircraft
Apart from the fact that most if not all pax will be carrying some type of Lithium Ion battery either in hand luggage or stowed luggage, as other posters have remarked;
There are several different types of LiIon batteries, with different chemistries.
The type most often used in consumer electronics is Lithium Cobalt or LiCo for short. This chemistry packs most performance in terms of energy density per unit volume and weight, but happens to be a bit touchy - as borne out in various incidents with laptop and mobile phone batteries catching fire.
Other chemistries such as Lithium Iron Phosphate (LiFePO4) do not have such a strong tendency to self-destruct in this manner, and in fact Lithium Iron Phosphate is now becoming the preferred solution for automotive and aerospace applications. However, energy density is somewhat inferior to Lithium Cobalt. On the other hand, Lithium Iron Phosphate cells appear to suffer less degradation with time/cycles.
Apparently (and regrettably) the B787's batteries seem to be LiCo rather than LiFePO4. The reasons for this choice are beyond me, but it might be that the choice was made some years ago when the performance penalty of LiFePO4 versus LiCo was more severe than it is now. 5 years is a long time in bleeding edge battery tech.