I had misunderstood Hokie's earlier response; I thought he was offering to give you the spring.
The Lionel number for the tower is 6-2324. The spring should be available from most Lionel parts dealers. S&W, Train Tender and Chuck Sartor are three who come to mind. Chuck is a regular here on the Forum. The spring part number shown in the exploded diagram Moonman posted earlier should also work on the LTI model tower you have.
Another thing you might try before buying a new spring is to remove some of the bands from the existing spring - shorten it in other words. If you choose to try this I will caution that "less is more". You can always remove more bands from a spring if necessary but, you darned sure can't add them back.
The info noted by Hokie and CW concerning the eyelet where the draw string passes through the wall is new to me. The graphite I've used over the years apparently has prevented any groove from forming. I checked my tower last night and there is no groove in the hole. I also long ago replaced the original line that came with the tower. For the past 20 years or so, I've used fishing line as the draw string for the stair guy.
And I will concur with CW's caution about graphite staining. You will have some staining inside the tower as well as in the stair guide. Fortunately, the staining inside the tower is visible only with the roof off and that inside the stair guide is normally hidden from view. In any event; this is why I say a smidge of the graphite. If some minor graphite staining will be an issue; definitely go with the eyelet instead.