As far as I know Rig-1 family proteins are activated only by double stranded viral DNA.
RIG family helicases are intracellular pattern recognition receptors, therefore can be activated only by intracellular molecules presented by intracellular pathogenic agents, in the case RNA viruses.
On the other hand, LPS is presented by extracellular Gram-negative bacteria and activates typically TLR4 and CD14 complexes in the cell surface.