The typescript compiler performs strict null checks, which means you can't pass a string | undefined variable into a method that expects a string.

To fix this you have to perform an explicit check for undefined before calling luminaireReplaceLuminaire().

In your example:

private selectedSerialForReplace(): string | undefined {
    return this.selectedSerials.pop();
}

luminaireReplaceLuminaire(params: {  "serial": string; "newserial": string; }, options?: any): FetchArgs {
    ............
}

const serial = this.selectedSerialForReplace();
if(serial !== undefined) {
    luminaireReplaceLuminaire({serial, newserial: response.output});
}

There's no isEmpty() method, you have to check for the type and the length:

if (typeof test === 'string' && test.length === 0){
  ...

The type check is needed in order to avoid runtime errors when test is undefined or null.

This is a simple function which involves the use of a function to evaluate the strings. This way you can remove the part of cases' "switch". Be aware that this handles also assignments to global variables, so I recommend it only if you know anytime where is the source from(don't allow users to use this function!)

var convertType = function (value){
    try {
        return (new Function("return " + value + ";"))();
    } catch(e) {
        return value;
    }
};

You can see the jsfiddle here.