Hi
Yes LAN is the bottleneck,If you move your Tape library to SAN then your disk array should be connected to SAN ,this to make sure that the data moving from disk Array to server which is attached to SAN network using HBA card,to increse the throughput you can use the serverless backup which moveing the data from Disk array to Tape library without even comes to the backup server,backup server will only initiate the backup,but you can't connect all your servers to SAN becuase this is going to be costly since you have Arcserve server,SAN Option and tape libray option installed in all machine connected to SAN,instead of going to SAN maybe if you use GIGABIT network this may increase the througthput.
Have a nice day
regards
mohamdr