  We study two types of dynamical extensions of Lucas sequences and give
elliptic solutions for them. The first type concerns a level-dependent (or
discrete time-dependent) version involving commuting variables. We show that a
nice solution for this system is given by elliptic numbers. The second type
involves a non-commutative version of Lucas sequences which defines the
non-commutative (or abstract) Fibonacci polynomials introduced by Johann
Cigler. If the non-commuting variables are specialized to be elliptic-commuting
variables the abstract Fibonacci polynomials become non-commutative elliptic
Fibonacci polynomials. Some properties we derive for these include their
explicit expansion in terms of normalized monomials and a non-commutative
elliptic Euler--Cassini identity.
