Board Thread:Lore Discussion/@comment-71.61.178.23-20130623221624/@comment-9887604-20130624120735

According to the pocket guide to the empire your assumption may be fairly valid. There is enough rooom to speculate that the Lilmothiit may have been related to Khajiit.

"In additional to the reptilian Argonians, who are today Black Marsh's most visible denizen, there were once tribes of men - Kothringi, Orma, Yespest, Horwalli - and tribes of mer - the Barsaebic Ayleids and the Cantemiric Velothi - and even a tribe who may have been related to the Khajiit of Elsweyr, the vulpine Lilmothiit." Pocket Guide to the Empire 3rd Edition 

Its also fair to note that they share the wanderers spirt with the Khajiit.

"The southern coastal regions, not surprisingly, were the realms of the Lilmothiit, though they were a nomadic group and left few enduring signs of their existence that were not covered up by later civilizations." Pocket Guide to the Empire 3rd Edition

Perhaps Lilmoth doesnt specifically refer to the city of Lilmoth, perhaps it is the Ta'agra(Khajiit language) word for swamp.