Are there any rules about not drinking alcohol in lent? What about in traditional Catholicism?
There’s actually a whole style of beer devoted to Lent that’s been around for hundreds of years. Many monks drank it to sustain themselves while fasting. 
No.
There is only one Catholic Church.
There is only one Catholic Church and she has no teaching banning alcohol in Lent or any other time
Hence the name ‘liquid bread’!
Potum non frangit jejunium = Drink (even alcoholic drink) do not breaks the rules of fasting.
Naturally being inebriated is sin.
It’s something you are certainly free to ‘give up’, but there are no requirements to do so.
The rules require abstaining from meat on Fridays except if a solemnity falls on a Friday and then fasting and abstaining from meat on Ash Wednesday and Good Friday.
There is no rule prohibiting alcohol. Jesus first miracle 1) was turning water into wine and 2) took place at a wedding signifying how important marriage is to the church.
There was no grape juice in biblical times. It is only recently that certain Protestant churches have claimed that alcohol is bad. Grapes naturally ferment into wine and to make grape juice one actually has to interfere with nature and stop the fermentation.
Also, most wine in biblical times had a higher alcohol content than the wine we consume today.
Sorry if that is more information than the OP requested.
If you are suggesting that there is only one fasting/abstinence rule within the Catholic Church, then you are mistaken. Byzantines have stricter fasting rules. Traditionally Byzantines wouldn’t even have dairy products during Lent, something that is allowed for Roman Catholics.
There is one Church, but different traditions within the one Church. There is such a prohibition on alcohol on certain days in the Byzantine Rite.
I am unaware of such a strict prohibition in the Roman Church. The RC doesn’t even prohibit dairy products.
That’s kinda what I was getting at when I said traditional Catholicism. For example I know some lent rules changed during Vatican II
One is either following the Catechism of the Catholic Church or one is not.
You may choose to be more precise, such as “before Vatican II” or “between the Council of Trent and Vatican II” when speaking of Latin Rite, commonly called Roman Catholics. Or you could be specific by stating Russian Orthodox Church, Greek Orthodox Church, the Byzantine Church, the Serbian Orthodox Church.
Saying ‘traditional Catholic’ is not precise. Ask a vague question, get a vague answer. Computer programmers call this practice "garbage in garbage out (GIGO)
The traditional strict fast in the East includes fasting from wine.