"Lionel" is also a line of electric model trains that was popular back in the day.

Sure does!

Well, believe it or not, people of prominence (or people aspiring to prominence) will name roads on their property, sometimes with their family names.
However, whatever way we slice it, whether the road is named "Twain," or the script is merely mentioning the house number in reference to "the Twain residence," the joke still works "Two Two Twain."
J'ai l'il AMRICAIN !

Here is what I see in the script, as quoted here on IMDB:
Sidney Wang: Look at invitation. What number of house?
Willie Wang: 2 2
Sidney Wang:
Correct. 22 Twain's
[choo choo train, i.e., Lionel Train]
Sidney Wang:
house. Continue.
S. Wang asked for the "number" not full the street address. He got an answer of 22 and agreed with it: "
Correct. 22 Twain's house. Continue.
" With his habit of dropping words that means "Correct. 22 [is] twain's house [number]. Continue [driving]."
Also:
Sidney Wang: [cutting him off] Never mind him, please. Here - you go up
this road
, past bridge to "22 Twain." No can miss it.
The quotes indicate he is referencing something, apparently the sign on the house, and is not giving an address in conversation. Compare to this:
Stan: Where does Mrs. Jones live?
Ollie: 123 Elm street. There is a sign, "123 Jones."
That is how I interpret the conversation in MBD and why I wonder if we ever heard the name of "
this road
," like
Lionel Twain
22 Mountain Road
Hollywood CA, 98765

Now, is there some dialog that actually claims that to be the address and not just a way to recognize the house?
You mean, besides the scene at the beginning of the movie, where Wang reads the address from a piece of paper: "Two-Two-Twain" ?
J'ai l'il AMRICAIN !

That's the very thing I am questioning. I'm not sure it is true. Just because the house has a sign that says "22 Twain" does not mean that "Twain" is the name of the street. We already know "Twain" is the name of the resident. It is possible, but unlikely, that the street and resident have the same name. Although the apparent prominence of the resident does make it a little more likely, that's not enough to clinch it.
For example, a mailbox that says "123 Jones" is probably for the Jones family at 123 of whatever street the mailbox is on. Putting the street name on the mailbox is a bit redundant. Evey box on the street might have the same name on it.
Now, is there some dialog that actually claims that to be the address and not just a way to recognize the house?

Hi robert
Twain's address is given at least once
At the beginning of the movie, as Wang and his son are looking for the house, Wang repeats the address
"Two Two Twain" as in "choo-choo train" !
J'ai l'il AMRICAIN !

Is 22 Twain really his address? If Maggie Smith lived across the street might she have a sign 23 Smith?
I wonder if the actual street name was given in the movie.

His name was definitely a spoof a continuation of the joke on the address "Two-Two-Twain" !
J'ai l'il AMRICAIN !

Not really based on anyone specific, just on the "wealthy eccentric recluse" character that shows up in a lot of mystery novels.