Your question was posted at 2am, so I apologize that there was not an expert available at that time. I am on the East Coast and usually shut down for the night at 10pm, but I am happy to answer for you now. This service works more like email than instant chat because we need a bit to do research on marks and value ranges. I do hope you understand.
We do one item per question, but I will do both of yours since you had to wait.
I would need one more photo of the mark on the lamp. The one you added was too blurry to read. Maybe back up a bit more to get it in focus. You can use the Add Files feature to add another photo.
The platter was made by Sigma of Japan in the Mikado pattern. This mark was used in the 1980's and 1990's, so it is not an antique, but is a pretty pattern. This platter has a value of $35.00.
I will wait to do the lamp until after you added a picture of the signature.