Since you opened this can of worms it is certainly important to address it. Standards wise, scissor lifts are regulated under the OSHA scaffolds standards and are considered "mobile scaffolds" , there is not a seperate standard for scissor lifts but there is one for boom type lifts. ANSI A92.6-2006 contains recommendations for scissor lifts.
Fall protection on a scissor lift has always been the guardrail, neither OSHA nor ANSI require a seperate "tie-off" with a personal fall protection system however manufacturers and OSHA specifically state that if PFAS is used, it is installed as a fall restraint system, not a fall arrest system. Simple physics - if an worker falls over the toprail, the lift could fall due to the horizontal forces applied. Even if the lift has a large platform thus minimizing the potential for lift turnover, the operator will get beat up by contact with the the scissor stack.
Your question seems to address that understanding since you are asking about tie-off outside the basket but wanted to get some reference info in first. The question to ask is why is the worker tying off in the first place. If they are climbing guardrails that is not allowed by ANSI, OSHA or the manufacturer. Oh, you mean real world were sometimes there is structure in the way which prevents the basket from going higher and the work area is out of reach and therefore the worker has to climb, ok, 2 answers.
1) During a preplanning phase this could be addressed - there are many configurations of lifts (scissor and boom) and one that is designed (size of basket) to manuver through, over, under the obstruction could probably be found - but we all know that usually you have to work with what you have, so
2) If the worker is going to climb over the protection of the guardrails (i am not suggesting or recommending this as it is a bad practice) then a seperate fall arrest system should be used. The worker needs to install the system before they climb (first man up system may work). And all the requirements for using PFAS needs to be followed. One important caution, if the worker falls and cant self rescue how do you get him down?
This is an issue (tie off in scissor lifts) that is burning up a lot of other blogs and safety groups. Which is unfortunate since workers fall OUT of scissor lifts is a small part of scissor lift safety. More lift turn over than workers falling out of them. Consider that a large lift weighs up to 30,000lb - think of the ground pressure created by the tires, holes, underground utilities, soft ground - yeah, that will bring even a large lift over if not seen during a pre-use inspection. Also, if you look at the manufacturers requirements the maximum wind velocity for the largest scissor out there is 28mph - you may recall the turnover fatality at Notre Dame - high wind. Also, most rough terrain lifts can't be used on slopes over 3-5 degrees and slab lifts have a 0 mph rating and must be used on firm level HARD surfaces (ie: concrete).
In a nutshell - the safety community is so concerned about tie off or no tie off in scissor lifts that all the other important issues (inspection, operator qualification training, use) are forgotten about. As a resource you might want to check out www.AWPT.org - lots of good information and training resources.
Hope that helps.
Hanover Insurance Group