Lassiter
English: habitational name from the city of Leicester (see Lester). This name has been long established in North America, and occurs in a wide variety of forms.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
Leister
English: variant of Lester.
German: occupational name for a maker of lasts or a cobbler, from Middle High German leist + the agent suffix -er.
Lester
English: habitational name from Leicester, named in Old English from the tribal name Ligore (itself adapted from a British river name) + Old English ceaster ‘Roman fort or walled city’ (Latin castra ‘legionary camp’).
English (of Norman origin): habitational name from Lestre in Normandy.
English and Scottish: variant of Lister.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
Lister
English: occupational name for a dyer, Middle English litster, an agent derivative (originally feminine; compare Baxter) of lit(t)e(n) ‘to dye’ (Old Norse lita). This term was used principally in East Anglia and northern and eastern England (areas of Scandinavian settlement), and to this day the surname is found principally in these regions, especially in Yorkshire.
Scottish: Anglicized form of Gaelic Mac an Fhleisdeir ‘son of the arrow maker’.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
Other Variants:
Leicester, Leycester, Lessiter , and Lisseter
Source: Sally's Family Place