Cutting down a spirea is not only going to be okay, but recommended to cut it down almost to ground level every five to eight years to renew the plant. However, if you are not having some major problem it will probably be better to not cut down either of them. The usual way to gradually renew a bush is to select either 1/4-1/3 of side branches or older stems to cut off. In the case of lilac after they bloom in the spring and in the case of spirea in the early part of spring before the sap is flowing (anywhere from about Feb-April depending on the year).