Upgrade the CPU in the Lenovo laptop

Assuming the new CPU fits the motherboard, absolutely. Of course, it could probably survive even a motherboard replacement as well.

Actually, no. A dual core processor is one processor with 2 cores, a quad core is one processor with 4 cores.. and so on.Hyperthreading dosen't come onto play yet

Lets take a 8 core processor, and have them on a hypothetical 8 processor SMP system. You have 8 processors with 64 physical cores . Hyperthreading lets you run 128 logical cores on them. Likewise the same setup with quadcores would have 8 processors with 32 physical cores, and with hyperthreading run up to 64 logical cores (which is the maximum in the windows server enterprise would be able to run).

Apparently in this case, a logical core is equivalent to the ability to run a thread.

EDIT: cleaned up the answer. Apparently i misunderstood it - the hyperthreading article on wikipedia was really useful here