Many thanks to Jamie for the following research on the Paper Mate pen prop seen on I Love Lucy. Says Jamie: “Lucy and Ricky as seen using a pen with a shiny top end and black lower end. I have identified this is a Paper Mate Deluxe pen, which came out in 1951 and pretty much revolutionized the ballpoint pen world. There is a great history page here: http://penshotsandthoughts.blogspot.com/2015/06/early-history-of-paper-mate-part-2.html
You can see on that page that it was even advertised by George Burns, Zsa Zsa Gabor and Gracie Allen!”
They are difficult to come by on ebay with the gold top, but there is one offered on eBay this week:

Vintage Early Model Paper Mate Ballpoint Pen – Black and Gold – Click here to see it on eBay

Following are various captures showing the pen in use on the show.