The two-fluid, Lawson-type ignition model of (Guazzotto and Betti 2017 Phys. Plasmas24 082504) for nuclear fusion concepts is extended to burning-plasmas. Numerical estimates for the Lawson product are obtained for different values of the gain factor Q and different plasma conditions. Namely, different assumptions are made for the various energy confinement times in the model and different density and temperature profiles are considered. It is found that it is easier to reach the burning plasma condition with peaked profiles. A technique for comparing pure-deuterium (DD) 'equivalent' experimental discharges with the predictions of our model for deuterium–tritium (DT) burning plasma discharges is described. This is done through the introduction of 'no − α' quantities using a procedure similar to the one used in inertial confinement fusion. Using tokamaks as a meaningful example, an experimental fit for the energy confinement time is introduced in the calculations and shown to have a considerable effect on the results, qualitatively changing the thermal stability of the system and the equivalent Lawson product estimates of pure deuterium plasmas. Moreover, if the energy confinement time depends on the heating power as in experimental scalings, the equivalent in DD discharges is higher than the corresponding in a DT plasma.