Someone once suggested to me that "Lot" is a play on the word "lehimalet" (See Bereishit 19:17(x2), 19, 20, 22) - or perhaps that should be that the verb lehimalet plays off the name Lot. Admittedly, a play on words does not necessarily reflect a real etymological connection.
It is an interesting theory - I've never seen it before. Certainly Lot was the first person to have the verb מלט -to escape -associated with him. Steinberg and Klein both point out that מלט -also to escape - is related to פלט - mem and peh, both labials, can alternate. In Modern Hebrew they've come up with a nice sounding phrase for input-output: kelet-pelet קלט-פלט.
Steinberg says that melet מלט - mortar (from Yirmiyahu 43:9) is related to the verb מלט, which can mean "to slip away", and mortar smooths the walls of a building (the verb חלק also means both "to be smooth" and "to be slippery".)
Lastly, as the title of this post hints, the name of the island country Malta may be related to the root מלט . As the Online Etymology Dictionary writes:
from L. Melite, perhaps from Phoenician melita, lit. "place of refuge," from malat "he escaped."