This has been proposed by a group of physicists, they called it LEP3.( LHC is in the tunnel of LEP and LEP2)
LEP3 would operate at 240 GeV at center of mass, and comprise two separate accelerator rings that would smash electrons and positrons rather than protons and protons, as with the LHC. In their study, the 20 authors call the concept for LEP3 "highly interesting" and that it deserves more detailed study. "Now is the right moment to get this on the table," says theorist John Ellis from Kings College London in the UK, who is an author of the preliminary study and hopes that it will trigger debate among physicists as to how to study the new boson in detail.
This would be enough to attain the Higgs region and get accurate values for standard model parameters. We had stopped at ~210 center of mass in LEP2 , and just missed the Higgs.
There is a proposal for a new tunnel for e+e- called TLEP. See this talk for a presentation .