Only one picture showed up, need to see the feet and back rail.
I can't but you can do a Google Image Search. https://support.google.com/websearch/answer/1325808?hl=en
Any labels, makers marks, or numbers? Do you have the mirror for the dresser?
There are so many lionhead armchairs photos online. Dresser looks like it may be a modern reproduction.
Both pieces are beautiful. There was a lot of attention to details when these were made. Practically impossible to find good quality today. I would begin by wiping down with a solution of equal parts of water and vinegar. Allow to dry and then use Murphy's Oil Soap according to instructions on bottle. The soap will clean all dust and debris, and the oil will condition the wood. Good luck.
The piece of furniture you are calling a dresser is a dry sink. The little bar on the back is where you hung the linen towels. The drawers were for extra towels and toiletries.
Beautiful chair! Nice dry sink too. They are probably 100 years old. That chair really needs to be cleaned (see Cindy's suggestions) and reupholstered with some plain (no print) fabric. I can't tell anything about the sink from the photo. If it has paint bits in the grain, it was painted and has been stripped. Just don't paint them, please!!!
Can't tell for sure, but the chair looks like a spring platform rocker. They were popular around 1900s. I even saw one on Bonanza!
What some are calling a dry sink, others would call a wash stand. It would have a large pitcher and bowl sitting on it with the towels (linen or flour sack) hanging on the bar. That is a beautiful piece.