Indeed, as several different units were fitted to these cars over the years. Broadly speaking they are a single cylinder around 125cc, or a twin cylinder 250cc. See below info.
LAWILThe Lawil S.p.A. is a former Italian automobile manufacturer that began production in 1967. Lawil was located in Pavia, Lombardia. Lawil S.p.A. was a part of the French Lambretta and the Italian Innocenti.
Composition of the brand name: Henri Willame (Director of the French Lambretta) + Carlo Lavezzari (Designer) = LAvezzari + WILlame
Following models were available:[1]
Lawil Farmer (S1) 123cc (1968-1971, F) / Lawil Varzina (S3) 250cc (1970 - 1980, ITA)
Lawil Farmer II 125cc (1975-1980, F)
Lawil Berlina (S4) 250cc (ITA) / Willam City (A1 to A3) 123cc and 175cc (1967-1971, F) / Willam City (A4 and A5) 125cc (1971-1980, F)
Lawil Pick-Up (C1) 123cc (until 1977, F)
Lawil Fourgonnette (C2) 125cc (1968-1988, only saled in F)
Lawil Break (C4) 125cc
WILLAM - refer to good resource
http://www.microcarfan.com/index.php/marques/74-willamCRAYFORDCrayford Willam Commuter car
The City - saloon with 5.6 hp 2 stroke Lambretta engine at £758
The Commuter - convertible with 5.6 hp 2 stroke Lambretta engine at £783
The City TC - Saloon with 12 hp Ducatti twin 2 stroke at £838
The Commuter TC - convertible with 12 hp Ducatti twin 2 stroke at £863