I see you added some notes to remaining ways in relation to this issue. E.g. in a note attached to https://www.openstreetmap.org/way/139269301 you say you removed the upper part of the Narva River as the river flows out of the lake.

This upper part that you removed however actually was not modelled as part of the Narva River, it was not part of respective relation, nor was it a named way.

As for cartographic principles, these deleted ways were treated the same as any other waterways passing any lakes, or river centerlines within river areas.

In general, it is arbitrary whether there is one river that runs through the lake, or whether there are two rivers, one flowing into the lake and another flowing out of the lake. In any case the actual network of waterways is continuous, and should be modelled as such.