You're right that "Otherwise," negates the Sufficient Condition (the condition to the left of the arrow) in the original conditional statement.
So, in the example about being able to make a definitive claim about the greatest bball player of all time, the original conditional statement would be:
"If we can make a definite claim about the greatest Basketball player of all time [THIS IS THE ORIGINAL SUFFICIENT CONDITION], it will be Michael Jordan [THIS IS THE NECESSARY CONDITION].
Otherwise [SUFFICIENT CONDITION NEGATED], I will go with Lebron James for my pick [THIS IS THE NECESSARY CONDITION, WE'RE TOLD, WHEN THE ORIGINAL SUFFICIENT CONDITION IS NEGATED]."
To diagram this, you would say,
"
Can Make Definitive Claimbest bball player of all time 
Michael Jordan"
"Otherwise," means you negate this sufficient condition. Negating this sufficient condition, you would say, "If we cannot make a definitive claim". But
you cannot assume what the necessary condition will be just from the use of otherwise; you cannot assume that the necessary condition when the sufficient condition is negated will be the logical opposite of (in this case, "NOT Michael Jordan") the necessary condition associated with the original sufficient condition.
For instance, in the context of this situation with basketball players, the second sentence beginning in "Otherwise," could have gone any number of different ways. It could have said, "Otherwise, I will go with Steph Curry" (I know literally nothing about basketball so I'm just picking a name that I hear in headlines a lot
); or it could have said, "Otherwise, I will not choose a player at all"; or it even could have said, "Otherwise, I will
still pick Michael Jordan."
"Otherwise"
only negates the sufficient condition (again, the condition in which we can make a definitive claim about the greatest bball player of all time) but doesn't necessarily mean the necessary condition (where we pick Michael Jordan) is negated (resulting in this person's NOT choosing Michael Jordan as the greatest bball player).
It would only be a
Mistaken Negation if you assumed that saying "Otherwise," (negating the sufficient condition)
also necessarily negates the necessary condition. In this case, that would be, if you assumed that Otherwise (in a situation where we CANNOT make a definitive claim about the best bball player of all time), we CANNOT pick Michael Jordan. If they are telling you that Otherwise (negated sufficient condition), they will select someone other than Michael Jordan (like LeBron James, or Steph Curry, or Kevin Durant -- again these names coming from someone who knows squat about basketball), that is not a
mistaken negation, but situation in which the speaker (on the LSAT, the rules on a LG or stimulus for an LR question) tells you that a negation of a sufficient condition yields a different necessary condition.
"If and only if", on the other hand, DOES tell you that, if we CANNOT make a definitive claim about the greatest basketball player (negated sufficient condition), then that person is NOT Michael Jordan (must negate the necessary condition as well). E.g., "If and only if we can make a definitive claim about the greatest basketball player of all time, we will choose Michael Jordan." This sentence tells you that If we can make such a claim, that person is Michael Jordan; if
not (i.e., if the sufficient condition does not hold), then the speaker would not choose Michael Jordan (although in this case we do not know WHO the speaker would choose, only that it's not Michael Jordan). In the scenario you presented, Lathlee, the "Otherwise," tells us whom the speaker will pick as the greatest basketballer of all time (in this case, LeBron James and NOT Michael Jordan) if we negate the sufficient condition. But you cannot assume, before reading the end of the sentence beginning with "Otherwise," that it is LeBron James or even that it is not Michael Jordan, since the speaker might still tell us he'd pick Michael Jordan whether or not the Sufficient Condition is met (i.e., whether or not a definitive claim can be make on this subject).
I can't necessarily name a particular LR question or LG rule that uses "Otherwise," but I came across quite a few in my prep. I feel like I saw some rules with consequences like this on sequencing games, but they were phrased differently. For example, "Either H is before J or H is before K, but not both."
That could be stated, assuming no two variables are at the same time as one another, as, "If H is
not before (i.e., after) J, then H is before K. Otherwise (as in, Sufficient Condition negated--H is before J), H is
not before (i.e., after) K." The way that I diagram rules like this, this rule just looks like,
J 
H K, OR K H J
However, it should also be noted that in this situation, you also need to be careful about the implications of "but not both," which allow us to create the conditional statement "If H is before J, then H is after K." So, not only MUST H be in front of one of them, H also CAN'T be in front of both of them.
Regarding LR, I feel like I've seen quite a few stimuli featuring this mechanism, often on Must Be True questions. The stimulus will contain one or more "if/then" conditional statements and also an "Otherwise," statement, in which a sufficient condition of one of the "if/then" statements is negated, and the stimulus then tells you the necessary condition of that negated sufficient condition, and then the question is "If the statements above are true, which of the following must be true on the basis of them?"
I wish I could point you to a specific example. Maybe the PowerScore folks have some in mind?
