I think the correlation is good, but coincidences DO happen, so you want to be as sure as you can be.
The fact that the IGI version of the census says born in Russia is helpful ... but where did THEY get it from??
Go back to the original document (FindMtPast allows you to see an image of the actual surviving Census papers ... and I imagine Ancestry must as well) and see what IT says.
If in any remaining doubt, or if it gives the Lancashire birth places, do an elimination search of the BMD registers. Are there any registered births which match? If so, invest in the certificates to satisfy yourself that the parents' names are different.
If there are NO matching birth registrations, then it is pretty certain that they were NOT born in Lancashire, no matter what the census says (just because it was written on a census return doesn't mean it was true ...).
Of course, proving that they were not born in Lancashire is not the same as proving that they were born in Russia (yes ... I know ... but Latvia was part of Russia at the time, was it not?) ... but it helps to strengthen the inferences that can properly be drawn from the coincidence.
Also, I think you need to check the shipping records. First of all, where did the Baltic traders tend to dock in Britain? Were they trading out of the East Coast ports, or were they trading out of Liverpool? I don't know, but I think this is important. If they were trading out of Liverpool then it makes sense that a family recently arrived from Latvia should be present in Lancashire; but if they were trading exclusively out of the East Coast ports, then this migration looks rather less likely.
A lot of the passenger lists survive, and the enhanced subscriptions at FindMyPast (and probably at Ancestry as well) give you access to them. If these children were born in Latvia, and you have them living in Lancashire when they were not yet in their teens, then you have a pretty narrow time band in which to search for their transit records. If you can find them, it should tell you when and where they arrived, and on what ship. Does that make sense, in the context of everything else you know about them? If so, then again, it is only inferential and not firm evidence BUT it is looking pretty good.
My gut feeling is that you are onto the right records here ... but gut feelings only take you so far. You want to find as much additional evidence pointing in the same direction as you can. And if the gut feeling is right then there SHOULD be further evidence. It's just a matter of finding it.
Good luck!
