Determining the fixed-target beam energy needed to produce some process and comparing that to the collider beam energy needed for the same process is a standard exercise that we give to particle physics students (and, indeed I give a simplified version of it to my modern physics students). It really only calls for special relativity.
But the result is that a fixed target experiment using one beam formfrom a collider is not half as energetic as a the collider experiment; it is a lot less energetic because much of the energy is thrown away in the form of the resultant spray having a large overall momentum in the lab frame. In other words, don't be thinking $6.5\,\mathrm{TeV}$ here.
There are exploratory plans to fund and build a electron-ion collider. Both Brookhaven and Jefferson lab are competing to get the nod using their existing facilities for one part of the infrastructure. (At RHIC they have the hadron beam, and JLAB the electron beam). But that is a two beam project.
Finally, the detector systems at the LHC are designed with proton-portonproton, proton-ion, and ion-ion collisions in mind. For electron-ion work you would build similar devices but some details of the design would be different.