A Lawvere theory is a category $T$ with finite coproducts in which every object is isomorphic to a finite coproduct $\amalg_{i = 1}^n x$ of a distinguished object $x$. Then a $T$-theory is a functor $T^{op} \rightarrow \text{Set}$.
This formalism can be used to model sets with algebraic operations on them.
Does this mean we can view a simplicial set as a $T$-theory, where $T = \Delta$?
No. The simplicial category $\Delta$ can be defined as the category of finite non-empty total orders, and its objects are not all coproducts of one object. Indeed any automorphism of an object of that category has to be the identity; but in any category the object $\coprod_{i=1}^n x$ has at least $n!$ distinct automorphisms (unless $x$ is initial or a quotient of an initial object, but this is not the case here).
Moreover, models of a theory $T$ are usually defined as product-preserving functors $T^{op}\to \mathbf{Set}$; but for simplicial sets there is no such restriction.