LLBLGen will use what ever connection string you specify in the configuration file, by default it is in key Main.ConnectionString. To prolong the timeout put a ; at the end of the string and then put
Connect Timeout = XX
or
Connection Timeout = XX
where XX is your timeout. I couldn't fully understand your question if you knew this or not. Doesn't hurt to say.
However if you are timing out only when using LLBLGen, that is very strange. I have never had any issues with it. The generated code connects to SQL Server probably the same way you would. I would check security and permissions to see if there are any deadlocks