rules

The lt rule checks if the value is numeric first. If one field is empty it's value will be null and thus it won't pass the initial check.

But the field is a required

Sorry I was wrong. The actual code is this:

// ValidatesAttributes.php
protected function requireSameType($first, $second)
    {
        if (gettype($first) != gettype($second)) {
            throw new InvalidArgumentException('The values under comparison must be of the same type');
        }
    }

So just do a dd() there to see what exactly the function is getting.

Why doesn't the required stop me?

Well that would be really difficult to say without seeing the form and the rest of the setup you have. I'll try it locally and come back to you.

So I've got it. If the less_than value is missing, then the required rule for the more_than is valid. Then the more_than will get to the greater than rule and try to access the less_than value, which is null and thus the types don't match. To make it work you have to make it a two stage check:

request()->validate([
    'more_than' => 'required',
    'less_than' => 'required'
]);

request()->validate([
    'more_than' => 'numeric|gt:less_than',
    'less_than' => 'numeric|lt:more_than'
]);

That would be the easiest way.

how can I write a two stage in request?

@SGUserFace what do you mean a two stage? Just write it exactly as I wrote it. It works. If any of the fields fail the first check you'll get the error immediately, else the request will be validated with the second set of rules.