Long-lived particles are predicted in many extensions of the Standard Model but the experimental detection is very challenging because they decay out of the first trackers and usually scape to the trigger decisions. In this work we review several new physics models and summarize the experimental status concerning the related searches. We revise the capabilities of the high level trigger system of the LHCb experiment and evaluate the effect of the trigger to detect long-lived particles for two models: a previous work where Dark Higgs Model is assumed, and another one studied for first time in this work, the Composite Higgs involving light scalars signatures. A Montecarlo study about the decay vertex proportions at reconstructible level is conducted, giving a general idea of how much information is missing from tracks downstream of the LHCb magnet. In the case of Composite Higgs model, a 60% of this type of vertices can be missed for lifetimes larger than 10 ps.