Not only LPS... but in general the dose required in lower species will be more as compared to higher species to produce similar effects, because of the difference in body surface area, mass and metabolic rate.
LPS is well tolerated by rodents, dogs and cats (Warren et al., 2010), but it is very dangerous for humans, causing septic shock (Yamamoto et al., 2011). Rodents are 1000-10000 less sensitive than humans due to special LPS binding proteins, but I do not know, if everything is clarified.
Warren TS, Fitting C, Hoff E, Adib-Conquy M, Beasley-Topliffe L, Tesini B, et al. Resilience to bacterial infection: difference between species could be due to proteins in serum. J Infect Dis. 2010;201:223-32.
Yamamoto Y, Harashima A, Saito H, Tsuneyama K, Munesue S, Motoyoshi S, et al. Septic shock is associated with receptor for advanced glycation end products ligation of LPS. J Immunol. 2011;186(5):3248-57.