I know it is usually stated as the threonine residue near the N-terminus of either light harvesting complex (lhc) b1 or lhcb2, but if this is somehow lost, say in a mutant, is the system flexible enough to compensate by phosphorylation at another site such as a serine residue or will state transitions just cease?
The protein in question from Arabidopsis has this UniProt entry. In the comments you read: The N-terminus of the protein extends into the stroma where it is involved with adhesion of granal membranes and post-translational modifications; both are believed to mediate the distribution of excitation energy between photosystems I and II. As known PTMs we have (see Sequence Annotations) Threonine-38 and Arginine-36; below you can see known mutations. My guess, though, is that they are a few years behind and so it's better to look at recent work.
Let us then take the PMID 11113141 referred to in the above entry and see the citing papers, e.g., via CiteXplore where I see at least a few relevant references on the topic of LHC phosphorylation. If there were a review, it would be listed there. Apparently, there is also a plant phosphorylation site database PhosPhAt which might help, see PMID 22723801.
In summary, not much is known, lacking even a single review on the subject.
is the system flexible enough to compensate by phosphorylation at another site such as a serine residue
If we are just talking about substituting a residue, I think that functionality would be dependent on the associated kinases. Perhaps the plant phosphorylation database rwst mentioned could be of help?
According to my biology book (S377 Book 3), threonine-serine kinases can usually phosphorylate both residues due to their similarity. There are also tyrosoine kinases, and hystidine kinases; the latter occurring in plants only. The book states that these are the only residues that are known to be phosphorylated. It is uncommon for a threonine-serine kinase to be able to phosphorylate tyrosine, but some rare kinases can do both.