Type Error with Default Value in Schema Using Literal Strings

Type error: Type '() => string' is not assignable to type 'LazyArg<"false" | "true">'.
  Type 'string' is not assignable to type '"false" | "true"'.

  10 |         include_family_list: S.optionalWith(S.Literal('true', 'false'), {
> 11 |           default: () => 'false',
     |           ^
  12 |         }),

Type error: Type '() => string' is not assignable to type 'LazyArg<"false" | "true">'.
  Type 'string' is not assignable to type '"false" | "true"'.

  10 |         include_family_list: S.optionalWith(S.Literal('true', 'false'), {
> 11 |           default: () => 'false',
     |           ^
  12 |         }),