Laser assisted adaptive optics systems rely on Laser Guide Star (LGS) Wave-Front Sensors (WFS) for high order aberration measurements, and rely on Natural Guide Stars (NGS) WFS to complement the measurements on low orders such as tip-tilt and focus. The sky-coverage of the whole system is therefore related to the limiting magnitude of the NGS WFS. We have recently proposed LIFT, a novel phase retrieval WFS technique, that allows a 1 magnitude gain over the usually used 2×2 Shack-Hartmann WFS. After an in-lab validation, LIFT's concept has been demonstrated on sky in open loop on GeMS (the Gemini Multiconjugate adaptive optics System at Gemini South). To complete its validation, LIFT now needs to be operated in closed loop in a laser assisted adaptive optics system. The present work gives a detailed analysis of LIFT's behavior in presence of high order residuals and how to limit aliasing effects on the tip/tilt/focus estimation. Also, we study the high orders' impact on noise propagation. For this purpose, we simulate a multiconjugate adaptive optics loop representative of a GeMS-like 5 LGS configuration. The residual high orders are derived from a Fourier based simulation. We demonstrate that LIFT keeps a high performance gain over the Shack-Hartmann 2×2 whatever the turbulence conditions. Finally, we show the first simulation of a closed loop with LIFT estimating turbulent tip/tilt and focus residuals that could be induced by sodium layer's altitude variations.