Yes 18" is what Lexus recommends for snow tires. Here are the specs to go by from Lexus :
Overall Size : 18 x 7.5
Pitch Circle Diameter : 114.3 mm
Offset : +40 mm
Center Bore 72.62 mm
Front : 225/45R18/18XL
Rear : 255/45/R18XL
The following two tires will work without any issues and should help you get thru the winter times :
Michelin Pilot Alpin PA2
Blizzak LM-18
Overall Size : 18 x 7.5
Pitch Circle Diameter : 114.3 mm
Offset : +40 mm
Center Bore 72.62 mm
Front : 225/45R18/18XL
Rear : 255/45/R18XL
The following two tires will work without any issues and should help you get thru the winter times :
Michelin Pilot Alpin PA2
Blizzak LM-18