Do I need the instructions to sell a LEGO set
You do not need the original instructions to sell a LEGO set, but including them makes the set easier to identify, easier to price, and easier to sell.
No. You do not need the original instructions to sell a LEGO set. A complete set of bricks and minifigures can be listed without the booklet. You should say the instructions are missing, in the same way you would say the box is missing. Buyers use the booklet to check the set number and to build the model, so a set with instructions sells more easily and usually for a bit more than the same set without them.
If you still have the booklet, put it in the parcel even if it is creased. Say whether it is original, complete, and dry. Torn pages, missing sheets, and water damage belong in the description. Photograph the front cover so the set number is visible. That single photo prevents a lot of "which set is this?" messages. Then start selling with the condition that matches the bricks, not a special condition just for the booklet.
Why buyers ask for them
The instructions are how many people confirm they have every part. Without them, the buyer is trusting your photo and your word. That is fine when the listing is precise, and it is a reason to price slightly under a copy that includes the booklet. For a retired set, the booklet also proves which version you have. Some sets were reissued with a different number or different minifigures. The cover settles that.
Digital instructions exist for a lot of recent sets, and some buyers are happy to use those. Do not rely on that as a reason to call the set complete with instructions. Say "paper instructions not included" and let the buyer decide. Older sets are less likely to have a free digital copy. If you are not sure, do not promise that the buyer can download them.
If the booklet is all you have
Instructions on their own are a weak listing unless the set is old and the booklet is hard to find. Most of the value is in the bricks and the minifigures. If you have the booklet and you think the bricks are in the loft, it is worth matching them before you sell the booklet alone. The set number on the cover is what you type into the checker on the homepage.
A booklet does not make an incomplete set complete. Parts missing are still missing. Use Used - Missing some parts and mention the instructions as included. The other way around is the same: a full booklet with a missing minifigure is an incomplete set that happens to include the instructions. Read can I sell an incomplete set so the condition and the price agree.
Packing the booklet
Slide the instructions into a plastic bag so they stay dry, and keep them flat if you can. Do not leave them loose against the edge of the carton, where a parcel sort will crease them. If you are also sending the original box, the booklet can sit inside that box, padded so corners do not cut the cover. Packing advice for the rest of the set is in delivery tips and in how to pack and post a set.
You keep the item price you set. Whether the booklet is included should already be reflected in that price. Compare with listings in the catalogue that mention instructions, and with the guide on pricing a used set. If there is a problem after delivery, Buyer Protection looks at what the listing promised, including the booklet.