1927 & 1930 Italy 5 Lire Contemporary Conterfeits?

I also don't think they are fake. Yes, there are edge letters for them but those letters were weakly engraved. I believe the edge letters had been worn out rather than "did not have the edge lettering" as you said, idmern.

From the pictures they look like the genuine stuff, so have to agree with 'wonghinghi'.
Just have a look with a 4x or stronger magnifying glass at the rim, the rim inscription can be very shallow and (nearly) worn away.
Also, how do they sound?
Btw, if they were contemporary counterfeits I would expect them to be cruder - and to make good quality counterfeits of them later wouldn't have been worth the effort.

Was this taken with a scale that's graduated to at least tenths of a gram? If the scale reads just in whole grams (like a postal scale or the like), your measurement doesn't tell much. They could be as high as 4.9 grams and the scale will read "4" in the latter instance. But if you're using a jewelry type scale, 4.0 grams would be suspiciously light.