Will An Ongoing Lawsuit Against Bank, Lender, Etc. Affect Recovery or Satisfaction
No, neither actions will affect the other while in motion concurrently. In short, lawsuits are a public action and recovery / satisfactions are a private action. However, once a remedy has been found privately this will affectly negate the need for a remedy in the public realm. As the primary example, a satisfaction of a mortgage will negate the suing of an entity for deprivation of rights in the execution, handling, or outright fraud committed with the promissory note.
NOTE: There is always the argument towards the recovery of funds paid towards the loan, but it is much quicker to keep using this process and profit versus a lawsuit that will take years to settle.