It doesn't need to be LPS, but OVA needs some sort of adjuvant to push for a response. LPS is to push for macrophage/dendritic cells to activate, leading to better antigen presentation and production of cytokines that would favor CD4 T cell activation and hence a CD4 memory response.

As for whether you can mount a T cell response to LPS...most likely not. LPS is a lipid/sugar molecule and isn't a protein, so it can't be processed into peptides for presentation. Even if there was... the TLR-4 response to LPS would be stronger and faster than any T cell response.