If they're the same height and same shade, you can get by with different ones. Hopefully, your tables arrive at mattress height and the lamps bring the total to 58-64" above the floor. You can lift a shorter one up on a stack of books to balance them out.

You don't have to, but to make it look nice without matching lamps takes more effort. With your matching nightstands you'd probably want to make sure your mismatched lamps were of similar height/visual weight and/or that they balance out other elements and relate in style to other furnishings in the space (so they look intentional and not hodge podge). I'm sure it can be done effectively by someone with a good eye, but if you don't have a lot of confidence in your abilities it would easier to get matching lamps ;)

Thank you for your responses! Unfortunately, the lamp I have is one of a kind (wish I had a pic to post). So could I do a lamp on one and something else on the other?

It's really about what you like an show well you can pull something off. If you are like me and buy everything in pairs, mismatched lamps might drive you batty. If you are like my friend with great artistic flair, you will know how to marry two different lamps os that they work together and look like a set, though not matching.

As an alternative to keeping the lamps similar size and scale, you could go really different for lighting on the other side. I've seen swag lamps used to good effect hung over nightstands, or you could you a sconce for lighting and keep the nightstand clear.

You can find a lamp in same/similar style category. But you don't have to use the same style. And yes, you could put something else on other stand if you like.

Ideas/inspiration:

If you can provide photos of the lamp and the bed/nightstands, someone can probably photoshop ideas for you.