I've read the first two volumes of Lagoon Engine (have the third, haven't read it yet), and the first volume, the only one in English so far, of Lagoon Engine Einsatz. LEE is not a sequel of LE, but they ARE companion manga and are related in some way. It's not clear yet exactly how the stories intertwine (it'll probably be made clear in later volumes), but hints have already been dropped.
In the first volume of LE, at the very beginning of chapter one, there is a person in Yen's dream with a long earring. The face is not shown, of course, but it seems like it might be Sakis. In chapter four, Jin, for a brief moment, catches a glimpse of a strange scenery and a long-haired figure wearing a cape. Again, the entire face is not shown but, again, it appears to be Sakis. Also, in LEE, Sakis catches a brief glimpse of a strange boy. The face is not shown (of course), but the boy's clothes are the same clothes Jin was wearing when he saw the strange scenery.
So far, that's the only link I've seen between the two stories. They even take place in different worlds. But I ain't complaining; they're both awesome manga.
And so are the rest of Sugisaki-san's series. Yeah, they ALL rock.