The $Lambda(1405)$ production in p+p collisions at 3.5 GeV and K$^-$-induced reactions is discussed. The shift of the measured spectral function of the $Lambda(1405)$ in p+p reactions does not match either theoretical calculations for p+p reactions or experimental observation in previous K$^-$-induced reactions. New experiments with stopped and in-flight $K^-$ are needed to study this initial state more in detail. The state of the art of the analysis is discussed.