Block copolymers offer an appealing alternative to current lithographic techniques with regard to fabrication of next-generation microprocessors. However, if copolymers are to be useful on an industrial manufacturing scale, they must meet or exceed lithography specifications for placement and line edge roughness (LER) of resist features. Here we use a field theoretic approach, based on the Leibler-Ohta-Kawasaki energy functional, to model the LER of lamellar microdomain interfaces in a strongly segregated block copolymer system. We consider a melt with a finite number of microdomains between parallel, template walls and derive formulas for the interface LER and sidewall angle variation (SAV) as functions of the Flory-Huggins parameter chi, the index of polymerization N, and distance from the template wall. Our perturbative approach yields explicit expressions for the dominant contributions to LER, namely, (i) an interface tension arising from the repulsive interaction between different monomer species and (ii) a stretching energy associated with the deformation of the polymers near an interface. Our results suggest that in order to meet the target LER goals at the 15, 11, and 6 nm nodes, chi must be increased by a factor of roughly 3 or 4 above currently realized values.