Chatelet-les-Halles and Chatelet are, practically, the same station. Geographically, the Chatelet-les-Halles RER station is between the "Les Halles" metro station at the North end and the Chatelet metro station at the south end. They are interconnected underground, however. CHatelet-les-Halles is physically closer to Les Halles than Chatelet. However, there is a travelator underground between the RER part and the Chatelet part of the station. If your exit is towards the southern end of Chatelet, it would make sense to follow the signs for line 1 when getting off the RER at Chatelet, as this is, IIRC, the furthest south of the metro lines at Chatelet. I would avoid following the signs for line 4 as there is a risk you might end up at the Les Halles end rather than the CHatelet end, which is not what you want.
You won't save much walking by changing at Gare de Lyon rather than Chatelet-les-Halles as, in both cases, you will have to walk from the RER part of the station to the metro part.
Perhaps giving the name of the street where your hotel is located would make it easier for a local (not me, though: too long has elapsed since I lived in Paris for me to be a reliable source
) to give you more reliable directions as there are multiple entry/exits to the Chatelet station and they can be quite remote from each other.