Translation:I have a lamp that is older than that one at my house.
"that is more old than" has 9 google results and "that is older than" 32,400,000 results. While "more old" and "older" may have the same meaning the use of "more old" in sentence construction is going to be very rare and seem odd to most people. Anyway when you see "más" always think if a "er" or "est" word could be formed with it when translating Spanish.
Many English speakers might use those interchangeably, but not all. That's a good example of translating the idea but not the words. On DL we are supposed to give as literal a translation as possible. When you get really good at it and are translating a casual conversation, that might be fine!