The answer to your question will be determined by what spcific code is in effect in your jurisdictiion and that may vary from community to community.
To compute the maximum lenght of a waste are you have to consider the type of fixture it serves and what is the minimum trap size for that fixture. In your case we are examining a bathroom lavatory that reqires an 1 1/4 minimum trap size.
The waste arm pipe must be a minimum of the trap diameter and a maximum of one trade size larger.
All drainage pipes under 3" require 1/4 in per ft pitch.
The bottom of the pipe at the trap weir may not be higher than the top of the pipe at the point where it attaches to the vent.
To compute the maximum length divide the pipe diameter by the required pitch and the answer is total feet of developed lenght of the pipe from the trap weir to the vent opening.
I.E. An 1 1/4 pipe divided by 1/4 inch per foot yeilds a maximum of 5 feet, however, there are a couple options you can consider on a lavatory drain.
If you increase the waste arm pipe one trade size to 1 1/2 inches the maximum lenght is now 1 1/2 divided by 1/4 = 6 feet.
There is another option that can be used on the lavatory. You can get a 1 1/4/ 1 1/2 trap. It is really an 1 1/2 trap with a reducing compression ring to fit the 1 1/4 tailpiece.
You would now have an 1 1/2 waste arm which would yeild 1 1/2 divided by 1/4 = 6 feet, or you could opt to then increase the waste arm pipe the permitted one nominal trade size which would be 2 inch.
2 inch divided by 1/4 inch would yeild a maximum distance of 2 divided 1/4 = 8 feet.
The Uniform Plumbing Code takes into consideration that a portion of the waste arm is filled with water therefore they have derated the maximum lengths.
Uniform Plumbing Code Maximum Trap Arm distance:
1 1/4" pipe 2 ft 6 in.
1 1/2" Pipe 3 ft 6 in.
2" pipe 5 ft