Lin sits next to the right of Bea.
'next to' here indicates how many positions to the right of Bea?
Grammatically, "next to the right of {thing}" means that there is a position to the right of the {thing}, and we are describing a position next to that. If "Lin sits next to the right of Bea" then Lin is two spaces away from Bea, because we assume we aren't saying that Lin is superimposed on top of Bea.
Idiomatically, do not do this. Native and fluent speakers do not use this construction. Just because something can be grammatically constructed with meaning does not mean it will make sense. What will happen is that the listener will be initially confused, and then possibly try to work through the rules of grammar to try to figure out what you meant. It's about as far from natural English as you can get.
Instead, use a similar phrase that more directly describes the location. What do I mean by "more directly"? Well, let's look at your sentence:
Lin sits next to the right of Bea.
Location 1: Bea.
Location 2: The right of Location 1.
Location 3: Next to Location 2.
This three step process is confusing and is the reason we don't say things like this. Instead, let's try:
Lin sits two seats to the right of Bea.
Location 1: Bea
Location 2: Two seats away from Location 1.
Much simpler, without having to chain locations together to understand what is being said.
This is not a correct idiomatic structure. You could say, “Lin sits to the right of Bea” or “Lin sits next to Bea, on her right,” but you cannot combine the two. If you want to clarify how far Lin is from Bea, you can use phrases like “right next to” or “two seats away from.”