The numerical approximation of incompressible fluid-structure interaction problems with Lagrange mul-tiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a computationally demanding coupled system at each time-step. For the case of the coupling with immersed thin-walled solids, we introduce a class of semi-implicit coupling schemes which avoids strongly coupling without compromising stability and accuracy. A priori energy and error estimates are derived. The theoretical results are illustrated through numerical experiments in an academic benchmark.