The majority of the value of a Handel lamp is derived from the shade. The same can be said about virtually all collectible lamps. The only reason Handel lamps are collectible is because of the artistic work that went into each shade. In most situations, the base is rather unimportant.
Customers were allowed to pick which base they wanted, so there is no standard base that is seen with a certain type of shade. Furthermore, it was a standard practice for years that customers could provide their own base and Handel would make a shade to work for it. So just because your base isn’t marked as Handel or isn’t original to the shade, is not really a big deal.
With that said, having a marked Handel base has certainly never hurt that value of a lamp. Authentic Handel bases are marked several different ways. Many bases left the factory with a felt bottom with a cloth tag that read Handel Lamps or simply Handel.
Plenty of other marking designations were used. We have a full guide to over 20 different marks that can be found on a Handel base or vase. Access the Handel mark guide here.
Handel did not start making their own bases until 1902. Any lamp made before 1902 will not have a marked base.