The effect of an external applied lateral tension on the line tension between two domains of different thickness in a lipid bilayer membrane is calculated. The thick domain is treated as a liquid-ordered phase in order to model a raft in a biological membrane; the thin domain is considered a liquid-disordered phase to model the surrounding region. In our model, the monolayers elastically distort at the boundary to create a smooth rather than steplike boundary to avoid exposure of the hydrophobic interior of the thick raft to water. The energy of this distortion is described by the fundamental deformations of splay and tilt. This energy per unit length of boundary yields the line tension of the raft. Applying lateral tension alters the fundamental deformations such that line tension increases. This increase in line tension is larger when the spontaneous curvature of a raft is greater than that of the surround; if the spontaneous curvature of the raft is less than that of the surround, the increase of the line tension due to application of the lateral tension is more modest.