(state) => { … } and state => { … } are equivalent, since parentheses are optional around single arguments in arrow functions.
state => lookup => { … } and (state, lookup) => { … } are not equivalent.
The first expression is a function that takes one argument and returns another function that also takes one argument, whereas the second expression is a function that takes two arguments.
An expression such as a => b => {return a + b;} is an example of currying. You can use both variants like this:
const add = a => b => (a + b);
add(2)(3); // 5
add(2); // function add/<() // This refers to the `b => (a + b)` part
add(2, 3); // function add/<() // Like above, because the second argument is ignored
const add2 = (a, b) => (a + b);
add2(2)(3); // TypeError: add2(...) is not a function
add2(2); // NaN // b isn’t provided
add2(2, 3); // 5
(state) => (lookup) => { … } would be equivalent to the first expression.
NB: (state) => (lookup) => { … } requires an explicit return to return the value; omitting the curly brackets { … } doesn’t.