Gaspar's original Time Egg

[Legend of the Past]

Is there any proof that Lavos did it?

Yes, the cutscene in the PSX remake.

[Zatopek]

so I have this question, if a Clone is used, Serge isn't killed thus there won't be dimension split right?

Yes, this sounds right.  

Keep in mind, though, Legend's theory that Kid used a Time Egg to save Serge much like was used to save Crono in CT is just a theory; I don't think there's anything to back it up from the game itself.  However, it is a very good way to explain the dimension splitting, that in failing to use a clone to replace Serge, Kid violated one of the major laws of Time Egg use.

[Zaperking]

When I saw the PSX scene, it didn't look like Lavos did anything. Chrono just like starts hovering and explodes pretty much Oo.

[Legend of the Past]

When I saw the PSX scene, it didn't look like Lavos did anything. Chrono just like starts hovering and explodes pretty much Oo.

Then you probably missed the part when Lavos opened his mouth... And prepared a ray... And shot it at Crono. You can download the movie from Chronicles to confirm it, it really shows Lavos blasting Crono.