Looking at the downloadable PDF, I find book 4 of De Mensibus (on the months) starts on p. 127 (p.50 of the printed text). It is devoted to discussing events in the Roman calendar, month by month, so starts with January. February starts on p. 138; March on p.143; April on p.153; May on p.163; June on p.169; July on p.171; August on p.178; September on p.182; October on p.184; November on p.185; and December on p.186. So the whole work is not very extensive.
IV.41 reads:
On day 11, the kalends of April, a pine tree is carried into the Palatine by the tree-bearers. But the emperor Claudius instituted these these ferias, a man of such justice in judgement that…
This event looks like the carrying of the sacred tree into the temple of Cybele. That the festival was created by Claudius again indicates the lack of Attis-related events in Republican times.
The short entry on December does not seem to mention Christmas, nor Saturnalia, nor any solar festival.
I can’t find any translations of De Mensibus, although a 1983 English translation of his work in 3 books on the Roman Magistrates exists, and a French edition and translation of the same work was made in 2006. An Italian version of another of his works. I’ve asked in the BYZANS-L if anyone is working on this text, and also emailed Prof. Jacques Schamp, who did the French translation of the Magistrates book.
The Italian transl of John Lydus is his De Ostentis, given the title “Sui segni celesti”. The transl is by E. Maderna, with an introduction by I. Domenici. Published by Medusa in 2007
Thank you very much — these sorts of details are always useful, particularly for anglophones who never know about Italian translations.