The time-domain passivity approach has been proposed in the literature in a variety of formats to guarantee the stability of teleoperation leader-follower systems. The conventional use of the proposed technique utilizes the control effort at the follower side as the force feedback to be sent back to the user at the leader's side. However, this has resulted in transparency problems, especially when the follower dynamics are not negligible. On the other hand, four-channel and three-channel Lawrence architectures have been investigated widely in the literature to maximize the transparency of the system when, in most advanced cases, stability is guaranteed using wave-variables. However, wave-variables are historically known for their transparency deterioration problems. In this paper, we propose a two-layer approach taking advantage of the fusion of (a) a more optimal derivation of Lawrence telerobotic architecture (utilizing only two channels), and (b) a two-port time-domain passivity stabilizer while comparing the performance with a one-port passivity stabilizer. The two-channel derivation of the Lawrence architecture allows for implementing a two-port time domain passivity approach, which is investigated in this paper. The performance of this is compared systematically through a multi-objective approach by analyzing dissipated energy besides force and velocity errors for a wide range of time delays and frequencies of excitation. The paper gives a comprehensive view of the efficacy of two-port versus one-port time-domain passivity control when combined with the two-channel derivation of Lawrence architecture.