Answer
You could use the mice to determine which TLR was responsive to LPS and, therefore, which one would need to be targeted by the drug.
Work Step by Step
The 2011 Nobel Prize in Medicine or Physiology was awarded for work along these lines. Mouse models with dampened TLR receptors were used to determine exactly what each type of TLR receptor responded to, leading to the discovery that each TLR type responds only to a specific set of chemical signals.