Well, clearly Lewis used mythological components in his stories - fauns, dryads, minotaurs, etc. - in the Chronicles. This was part of Tolkien's complaint against Lewis, that the Chronicles weren't their own self-consistent reality, but poached from other legendary frameworks indiscriminately.
In doing so, Lewis sometimes subtly changed the aspects of these beings, perhaps to make them more palatable to his target audience (i.e. modern youth). For instance, in classical mythology beings like fauns and centaurs had temperaments that suited their physiologies. Being half man, half beast, they were coarse, impetuous, and at the whim of "animal" instincts (rage, lust, etc.) Their presence was rarely a good sign - for instance, fauns were the companions of Pan, and they usually brought with them frenzied mayhem (from which we get the word "panic"). The Romp in Prince Caspian is a glimpse of this, but a much tamer version - the reality was often a drunken, violent orgy.
So there were clear parallels, but very much toned down. In fact, I grew up with this vision of "tame" centaurs, dryads, and the like, and was startled to learn later in life that the classical picture of these beings was very different. Interestingly, J.K. Rowling in the Harry Potter series portrays centaurs much more like their classical personalities, though even she tempers them a bit.