They're 14" to the socket, the metalic base is 6" by 6. The marks are on the bottom of the figurines.
I was able to find it when I rewired it. The item "RARE Antique E&A Muller German Set of 2 Table Lamps Children & Dog Figurines 14" is in sale since Saturday, October 24, 2020.
This item is in the category "Collectibles\Lamps, Lighting\Lamps". The seller is "something_beautiful_17" and is located in Mount Prospect, Illinois.
This item can be shipped to United States, Canada, United Kingdom, Denmark, Romania, Slovakia, Bulgaria, Czech republic, Finland, Hungary, Latvia, Lithuania, Malta, Estonia, Australia, Greece, Portugal, Cyprus, Slovenia, Japan, China, Sweden, South Korea, Indonesia, Taiwan, South africa, Thailand, Belgium, France, Hong Kong, Ireland, Netherlands, Poland, Spain, Italy, Germany, Austria, Bahamas, Israel, Mexico, New Zealand, Singapore, Switzerland, Norway, Saudi arabia, Ukraine, United arab emirates, Qatar, Kuwait, Bahrain, Croatia, Malaysia, Chile, Colombia, Costa rica, Panama, Trinidad and tobago, Guatemala, Honduras, Jamaica, Barbados, Bangladesh, Bermuda, Brunei darussalam, Bolivia, Egypt, French guiana, Guernsey, Gibraltar, Guadeloupe, Iceland, Jersey, Jordan, Cambodia, Cayman islands, Liechtenstein, Sri lanka, Luxembourg, Monaco, Macao, Martinique, Maldives, Nicaragua, Oman, Pakistan, Paraguay, Reunion, Uruguay.