To support the increasing number of planned lunar missions, a collaborative international initiative is underway to conceptualise and establish a lunar satellite constellation for communication and navigation. In this context, the goal of the current paper is to analyse what the obtainable performance is for a lunar lander that executes state estimation employing one-way ranging signals from such a Lunar Navigation Service (LNS). In particular, a small-sized optimised navigation constellation is considered as the main source of measurements, which, coupled with an accelerometer and an altimeter, is used to estimate the lander absolute trajectory during the main braking phase. The guidance is extracted on board by interpolation of a ground-optimised trajectory, followed by a reference-tracking regulator. Two alternative control tuning cases are presented, one targeting high performance, the other targeting low propellant mass. Nominal performance and associated sensitivity analyses assessed the feasibility of supporting such a critical phase with a reduced LNS constellation, reaching final control errors below 500m, with the better performing one going down to 56m. Among the two proposed alternatives, the one targeting low fuel expenditure has proven, however, to also be more robust against time and state uncertainty, providing much larger success rates.