A system for operating a cylinder valve assembly for an internal combustion engine comprising: - a main event motion source configured to provide main event valve motions to the valve assembly, - a main rocker arm operatively connected to the main event motion source, in such a way to assume an active condition at main event and a released condition, - a lost motion assembly (LMA) operatively associated to the valve assembly (VB), wherein the lost motion assembly includes an outer plunger (OP) arranged to receive a main rocker arm action and to transmit such action to the valve assembly through a locking element (LE), wherein the locking element is arranged to assume - a locking condition with a first portion disposed in a corresponding seat (LES) of the valve assembly and a second portion disposed in a passing through opening of the outer plunger, - an unlocking condition where the locking element is completely outside the seat (LES) of the valve assembly, wherein the outer plunger includes a first duct (LD) to convey a hydraulic medium, arranged to pressurize the seat (LES) and wherein the lost motion assembly is realized such that sliding force exerted on the locking element by the corresponding seat pressurization exceeds frictions developed between the locking element and the corresponding seat only when the rocker arm is in released condition, wherein the locking element is forced to return in the locking condition by a first spring (IPS, RS) acting directly or indirectly to the locking element, wherein said outer plunger includes a bore (B) to which an inner plunger (IP) is associated and charged by said first spring (IPS) according to a direction (X) transversal to the locking element movement between the locking and unlocking condition and wherein the inner plunger includes a recess (IPR) to receive the locking element to assume said unlocking condition and wherein said recess is shaped to force the locking element to assume said locking condition when a reciprocal movement of the inner plunger with respect to the outer plunger is caused by said first spring (IPS), the system being characterized in that said inner plunger is suitable to be actuated by pressure generated by a second duct (CD) suitable to convey the hydraulic medium, such that to push the inner plunger against said first spring (IPS) and in that , said first duct and said second duct are reciprocally communicating so that, when pressurization happens, the inner plunger lowers compressing the first spring (IPS) and facing the recess (IPR) to the locking element, such that the locking member slides in the recess causing the unlocking condition. - a main event motion source configured to provide main event valve motions to the valve assembly, - a main rocker arm operatively connected to the main event motion source, in such a way to assume an active condition at main event and a released condition, - a lost motion assembly (LMA) operatively associated to the valve assembly (VB), - a locking condition with a first portion disposed in a corresponding seat (LES) of the valve assembly and a second portion disposed in a passing through opening of the outer plunger, - an unlocking condition where the locking element is completely outside the seat (LES) of the valve assembly, <EOS>