This is what I've done:
Blocking secure.logmein.com in all of it's IP addresses wasn't enough as the program was connecting to changing IPs in the range 212.118.234.0/24 with a PTR to unkown.logmein.com
So my final iptables implementation looks like this:
-A FORWARD -s 74.201.74.193/32 -j REJECT
-A FORWARD -s 69.25.20.193/32 -j REJECT
-A FORWARD -s 77.242.192.193/32 -j REJECT
-A FORWARD -s 92.242.140.1/32 -j REJECT
-A FORWARD -m iprange --src-range 212.118.234.1-212.118.234.254 -j REJECT
-A FORWARD -d 74.201.74.193/32 -j REJECT
-A FORWARD -d 69.25.20.193/32 -j REJECT
-A FORWARD -d 77.242.192.193/32 -j REJECT
-A FORWARD -d 92.242.140.1/32 -j REJECT
-A FORWARD -m iprange --dst-range 212.118.234.1-212.118.234.254 -j REJECT
I also implemented the GPO which apparently does nothing, but when you try to access from the LogmeIn webpage, it returs access denied.