Looking at your X-ray, you need not only a crown but also a root canal. Unfortunately, your tooth/filling is broken as such that has caused a nerve damage. Therefore first a root canal needs to be done to remove the damaged nerve and seal the canal to prevent you from getting an infection. After, you need to support the tooth so upon chewing you wouldn't break the tooth any further. Since doing a root canal will hollow out the tooth further you really need a full crown to hold the tooth together and prevent further fracture. If you hadn't needed the root canal one could have restored the tooth by doing a partial crown (Onlay) in order not to touch or shave the part of the tooth that is intact. You can ask for a cosmetic crown which looks pretty natural. Hope this answers your question
The Root canals done on lower Anterior teeth are often restored with just a filling since the access for root canal is very minimal and the damage to the tooth is very minimal. The only reason one may need a veneer or a crown is if the tooth has changed shade (For cosmetic reason) or was decayed badly. In your case if you didn't have a cavity and you are happy with the color of the tooth it's best to restore it with a filling and be conservative.
