What are the other language models of computation similar to lambda calculus?
Yes, there are many models of computation, and of those many are extensions or modifications of the $\lambda$-calculus. You may wish to learn about partial combinatory algebras, which are very general models of computation, of which the $\lambda$-calculus is an example. Every partial combinatory algebra has a $\lambda$-like notation for defining functions. They encompass examples such as: $\lambda$-calculus, Turing machines, Turing machines with oracles, topological models of computation, PCF, etc.

Many models of computation can be seen as extensions or modifications of the $\lambda$-calculus. Let us consider the simply typed $\lambda$-calculus augmented with various features:


System T is $\lambda$-calculus with natural numbers and primitive recursion. It is not Turing complete.
The aforementioned PCF is $\lambda$-calculus extended with natural numbers and general recursion. It is Turing complete.
There are many extensions of PCF, for instance PCF++ can perform parallel computations, PCF+catch can throw and catch exceptiosn, PCF+quote can disasemble code into source code, etc. These are all different computation models based on the $\lambda$-calculus.
In another direction, we can extend the $\lambda$-calculus with more powerful types, for instance System F is a $\lambda$-calculus with polymorphic types. It is quite powerful but not Turing complete.


All of this is just scratching a rich theory of models of computation and functional programming languages (which is what extensions of $\lambda$-calculus are, more or less). If you are interested in the topic, you can start by reading some books on the principles of programming langauges (for practical aspects), or some books on realizability theory (for theoretical aspects).