Although both the transport barriers in the plasma interior and edge, namely internal transport barrier (ITB) and H-mode, are simultaneously required to sustain high-β and improved confinement in steady state, experimental observations suggest that theL-H transition and ITB formation are independent phenomena with different formation conditions, and they often exhibit apparent contradictions to each other. Accordingly, the compatibility conditions of edge and internal barrier formation have been investigated in JT-60U. The L-H threshold power is substantially increased in strong ITB plasmas, and high-performance discharges often persist in L-mode. On the other hand, the ITB formation power increases in H-mode plasmas. It was found, however, that the L-H transition criteria expressed in terms of the edge quantities are similar in plasmas with and without the ITB, and the edge density is extremely low in strong ITB plasmas. It has also been demonstrated in JT-60U that the controlled degradation of the ITB quality, in terms of the changes of toroidal torque input, results in an increase of edge density and induces theL-H transition. Therefore, the quality of ITB modifies the L-H transition threshold power, indicating that the additional `hidden' parameter is present in ITB plasmas. Other approaches of dynamically controlling the L-H transition in ITB plasmas, such as the triangularity ramp developed in JT-60U, are also discussed in this paper.