Hey, I'm a bit new to these errors, but from reading it I'd say maybe its the amount of memory you have allocated to minecraft. Have you ran this mod pack before? Can you put more memory towards minecraft and see if that works? What was this mod pack's name? Have you looked up the name of the pack to see if anyone else is having similar issues?
I have put together a group of mods that I'm messing around with using forge. After a few minutes a spike of lag appears and lasts for a few seconds and the game continues normally until the next lag spike. So far I don't see any specific time or place this occurs. I have about 8 gigs of ram allocated to Minecraft, when the spike occurs the usage jumps up from 20% to 99% . Minecraft is being run on 1.7.10. My question is there a way to tell what mod is causing this issue without having to go through each mod and testing it?