Thanks for your question. Most of the HA fillers of today contain lidocaine. If you have a sensitivity to lidocaine, it is not hard for your provider to have some product without lidocaine – they may need to order it if they do not have it in stock, but many keep some for patients who are lidocaine sensitive.
I assume you may be allergic to lidocaine which is very rare but if you are your doctor can get Restylane without or use Belotero which is a hyaluronic acid filler without lidocaine