Yes there's a huge advantage to having an All-Lumber city!
First of all, lumber on most servers sells for more than Iron so for any lumber you produce if you sell it and buy iron you'll get slightly more iron in return.
Second, saw mills take less population to run than iron mines. Thus you need less cottages and thus you can have more barracks in your city for faster troop training times.
Third, you actually produce more resources if you produce only one type of resource in each city. If you want to understand the math I've discussed it below.
The Math:
A valley ups base production by a %. If you have more than one valley that percent is added together then applied against your base production.
Formula:
total valley bonus (in resources) = base production x valley bonus x # of valleys
Example:
180000 x 23% x 10 = 414000 (lumber)
total production = 180000 + 414000 = 594000 (lumber)
Now if you were to split your production and valleys down the center to make iron and lumber in the same city it would look like this:
Example:
90000 x 23% x 5 = 103500 (lumber)
wood production = 90000 + 103500 = 193500
90000 x 23% x 5 = 103500 (iron)
iron production = 90000 + 103500 = 193500
total iron + lumber production = 193500 + 193500 = 387000
As you can see you make considerably more total resources when we only produce one type of resource in every city we own.