Iterative lengthening search: iterative version of Uniform Cost Search or DFS?
Typically iterative deepening searches are used with DFS to improve the memory usage.

Consider BFS and IDDFS, both are optimal and complete but IDDFS in a tree search will use only $O(bm)$ space, where $b$ is thebranching factor and $m$ is the maximum height of the goal.

Now extending this to Uniform Cost Search using DFS, if we increase the max depth step by step, we are doing too many iterations over already visited nodes, whereas this was not true in case of IDDFS because of one step increase at a time (look for the overhead factor). So though using iterative search with DFS can save huge space ($O(bm)$), it gets worse with time complexity. 

Secondly, there is no point in using Iterative Search with UCS as it is never a better upgrade over simple UCS in terms of space and time complexities.