The fact that when changing the object from a Printer to a Windows machine has a different outcome doesn't surprise me (much...) since those are two distinct scans. A printer has SNMP (or maybe just protocol scans) and a Windows machine uses WMI...
Also, and regarding the ping behavior, remember that the red/green dot represents a ping done from the Lansweeper server to the IP, and the Ping action is a ping from the machine where you are running the web browser to the IP. If you running the web interface on the server OK, it should be the same. If not, them there could be a world of possible issues, firewalls, network ACLs', etc
Forgive me for asking some basic questions:
1) Is the printer connected via DHCP or Static IP ?
2) Are the DNS entries for the same IP ?
3) With the printer connected, could you do a "nslookup <printer IP>" ? Does it always return the same IP ?
To be honest, your description of the issue points to having some other device on your network with the same IP than the printer, OR Lansweeper thinking that the name is to another IP... something that Lanswweper can scan, but not a Windows machine... don't be so sure that Lansweeper doesn't use DNS or reverse DNS, it does... check for instance "Scanning->Scanning Issues->DNS Errors"