Edit: 

Well, it looks like I found the culprit for the crashes.......and it is dumb
As it turns out, my instinct was right in that nothing was wrong with my PC or programs (as the world runs fine in single player) and that it was not a network play error (As other worlds played fine). Instead, I investigated why the wrold crashed when my partner joined. On a hunch, I deleted her playerdata from the LAN world, had her spawn from zero, and the game run smoothly. I then restored her playerdata and had her remove all items and place them in a chest. Again, a smooth run. THen, by slowly adding the items back, it turned out that the three maps (max zoomout) she had with her and used them to explore the areas for our big map at home base (Had four maz zoomout maps mapped already) was causing the crashes. After troubleshooting more, however, it did not seem one singular map was the culprit; instead, when she had multiple maps in her inventory, THAT would cause the crash. Now tested with just one map, mostly runs fine. Seems that the more maps she has in inventory, the higher the crash on save chance.

I am not sure what the exact bug behind this is, but I am sure some of you might find it interesting, and if Mojang is listening in, it might be a future bugfix. For now, I am just happy I get to play LAN with my partner again.

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What it says in the title, minecraft freezes and crashes when "Saving World" in LAN specificaly. Allocating aditional memory (given 12 GB, the game only ever uses up to 7 or 8 at most) did nothing (somewhat helped in Single Player with random crashes, but no help in LAN). I have been tracking processor, RAM and graphical usage using Task Manager while the game is up, and there are never any significant spikes in any of the three before the crash happens, the CPU usage of Minecraft just suddenly drops to 0% as it freezes when the server autosaves the LAN world or I "Save and Exit" manualy. As mentioned, I have allocated aditional memory to Minecraft and it never happens that my PC reaches its maximum usage in any way. The gme for some reason seems unable to sve the world anymore. We used to be able to play the world just fine untill about a week or so ago when this started happening. Is there anything I can do about it? I do not want to have to start another world, especialy if I do not know if this will happen again at some point