The Pila IBC charger bays are designed to take 18650, 17670, 18500 and 17500 cells.
The charger delivers 600mA to each bay, so it should not be used to charge cells which have a capacity lower than 600mAh. This makes the charger borderline for use with R123s, which will fit with an extra spacer, and 14500s. Bear in mind that despite some claims made for high-capacity R123s (1,000mAh etc) these claims are complete BS, even if it is printed on the cell. There are no R123s that have a capacity greater than ~750mAh.
Always be careful when charging Li-Ions, as this is when accidents are most likely to occur. A sure sign of trouble is if a cell heats up during charging. Warm is OK, but if it gets hot, stop the charge immediately or it could explode. When cells get old, or if they have been overcharged or repeatedly fully discharged at high currents, they become marginal and lose some capacity.