No BLEXBot is not google. It belongs to a company called WebMeUp. You can find information about them here.
If you lookup the IP in the log you will see it's not Google.
IP Address 198.143.187.122
Host blexn3.webmeup.com
Location US US, United States
City Chicago, IL 60661
Organization SingleHop
ISP SingleHop
Google IPs will list Google as the organisation.
Google use their own Bots, they are custom built. You can read up about them here, including a definitive list of their user-agent strings which may be useful to you.
To block follow the instructions here.