Here is a picture from the Palace of Governors in Santa Fe. There is a lance in the top right corner. Unfortunately taking pictures is prohibited and thus the quality of the picture is somewhat poor, and there is no close-up.
This is too bad, because the lance is really pretty - it features a silver inlay with floral design. I am not sure if it was locally made or imported from Spain. The socket is flattened to make it into a tang.
There are some other nice items in this display, including an espada ancha (with active rust in the fullers
) and a buffalo hide shield, called "adarga".