Arbitrary is not the same as subjective; as a matter of fact, they are pretty much opposites. Subjective means it is based on personal feelings, opinions, and beliefs.
1. influenced by or based on personal beliefs or feelings, rather than based on…
dictionary.cambridge.org
Arbitrary is pretty much the opposite, meaning random, compulsive, or unpredictable. IOW not thought out.
existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will; based on or determined by individual preference or convenience rather than by necessity or the intrinsic nature of something… See the full definition
www.merriam-webster.com
IOW a subjective claim is thought out, an arbitrary claim is not thought out.
Don't subject yourself to more confusion—learn the difference between "subjective" and "objective" right now and always use them correctly.
www.dictionary.com
As you can see from the the above definition, if you have to incorporate extenuating circumstances in order to determine if it is a lie or not, those extenuating circumstances are based on your personal perspective, opinions, and beliefs; making the behavior subjective.
For example; if I told you eating a 500 mg cyanide tablet will kill you, this is an objective claim. It doesn’t matter if you’ve eaten it by accident, or if you did it to save the life of another person, consuming 500 mg of cyanide will kill you regardless of extenuating circumstances. That is an objective claim
If you have to look at all the circumstances around a behavior (in this case the lie) in order to determine if it is good or bad, by definition that behavior cannot be objective; it has to carry the subjective label.