It doesn't matter what we think OP. If you're comfortable with the level of care she provides, then let her go. In my opinion, your nanny sounds lazy. Some children do sleep more than others, but not getting them out for any activities or playtime is unacceptable. Her lying about it is a big red flag.
Sometimes children do things beyond our control ( baby sleeping late so we miss a class, etc), but you decide how you want your children to spend their days. I would look for a replacement.