Partition of a unity on infinite-dimensional manifold of the Lipschitz class $\mathrm{Lip}^k$

We prove a critrion of $\mathrm{Lip}^k$-paracompactness of infinite-dimensional manifold $M$ modeled in nonnormable topological Fréchet vector space $F$. We establish that for $\mathrm{Lip}^k$-paracompactness it is necessary and sufficcient for the space of models $F$ to be paracompact and $\mathrm{Lip}^k$-normal. We prove suffcient condition of existence of $\mathrm{Lip}^k$-partition of unity on a manifold of class $\mathrm{Lip}^k$.