explains that dating pianos purely on the basis of numbers is often not as simple as it seems. There are usually several numbers inside a piano, and even if 3110 is the correct serial number, we cannot date it, because no Lipp numbers that low are published.
If your tuner thinks it is safe to remove the action (the working parts of the notes) it may be marked on the back with the action makers' name and number, and I may be able to date this.
Does the piano have any information about dates when they received exhibition medals?
If you are able to attach photos here, or email them to me, to show what the whole piano looks like, I may be able to tell you more.
Email via my website.
If you find old references or links on this site to pianogen.org, they should refer to pianohistory.info