"LAN access from remote" log entries

shadowserver.org is a bunch of folks who (from Wikipedia): "The Shadowserver Foundation is a volunteer group of professional Internet security workers that gathers, tracks and reports on malware, botnet activity and electronic fraud. It aims to improve the security of the Internet by raising awareness of the presence of compromised servers, malicious attackers and the spread of malware."
And Rapid7 is an Internet security company.

I don't know what they are doing scanning or trying to access your network, but are you sure your local network has not been compromised/part of a botnet, etc..?
BTW, I am an utter nobody and know-nothing-much, and I'm sure someone with Real Smarts can assist you better, but I'd just check your local PCs/devices anyway.
The one time I had something like this happen was when a friend's son used his laptop on my home network. When he wasn't using it, the botnet he been infected with started doing its nefarious deeds. I booted him off the network, cleaned his laptop, and his mum bent his ear for months of his obsession with visiting absolutely any site that said they had "Game Cheats."
Teenagers, huh? ;)

Hope someone can really help you.
Susi xx