The connection between Lorkhan and Jyggalag is thoroughly established by the circumstantial evidence, even if someone like MK hasn't come and said it outright as he has with the connection between Lorkhan and Akatosh. Jyggalag is exactness, the Spirit of Limitation that had to be suppressed in order to allow Nu-mantia. Jyggalag was necessarily changed by the removal of Lorkhan's heart, because it was his heart too. And if you still have doubts, consider Arden Sul.
Mehrunes, Hermaus Mora and possibly Meridia were changed or made as a result of creation. In the Monomyth it is described as:
The Daedra were created at this time also, being spirits and Gods more attuned to Oblivion, or that realm closer to the Void of Padomay.Jyg/Sheogorath fits in this category as well. Jyg is predictability, Dyus talks about it. Mundus however was created to be always new, unpredictable. The Champion of the Isles shows this by prevailing contrary to all prediction. In other words, the concept of complete predictability could no longer exist in a world that had become unpredictable. Hence the birth of an unpredictable schizophrenic manic depressive mad god.
Under the assumption that the myth of Arden-Sul retells how a new Sheogorath is born, the two stories reflect the Merish or Manish versions (sort of) of the death of Lorkhan. As in Faith of the Empire, this would imply that the death of Lorkhan triggered the transformation of Jyg into Sheogorath. (Not the Daedra as Jyg claims!) In this situation, there is no special relationship between Lorkhan and Jyg. No more special then his relation and any of the other Daedra that were changed in creation.
Though if you must assume that there is, then assume Dagon instead of Peryte. Then you have a story of how Lorkhan triggered Jygallag into Sheogorath and Alduin triggered Leaper into Dagon. The two still have no relation but atleast it's less jarring then Peryte being a Dragon.
That all the Interplay is one flea of assertion on a wolf of naught, and that every experience (that is, everything) born from that primal wail would cascade unto the echo-need of hologram, each slice the same except for scale - http://www.imperial-library.info/obscure_text/sporedream.shtml
This is an important key point. In each level of creation be it Anu vs Padomay, Oblivion vs Aetherius, Lorkhan vs Akatosh, Cyrus vs Tiber, Nerevarine vs Dagoth, Martin vs Mankar, you can find this duality. There is no room for a two by two relationship.