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The ferromagnetic (FM) nature of the metallic LaCo$_2$P$_2$ was investigatedwith the positive muon spin rotation, relaxation and resonance ($\mu^+$SR)technique. Transverse and zero field $\mu^+$SR measurements revealed that thecompound enters a long range FM ground state at $T_{\rm C}=130.91(65)$~K,consistent with previous studies. Based on the reported FM structure, theinternal magnetic field was computed at the muon sites, which were predictedwith first principles calculations. The computed result agree well with theexperimental data. Moreover, although LaCo$_2$P$_2$ is a paramagnet at highertemperatures $T>160$~K, it enters a short range ordered (SRO) magnetic phasefor $T_{\rm C}<T\leq160$~K. Measurements below the vicinity of $T_{\rm C}$revealed that the SRO phase co-exists with the long range FM order attemperatures $124\leq T\leq T_{\rm C}$. Such co-existence is an intrinsicproperty and stems from competition between the 2D and 3Dinteractions/fluctuations.

Co-existence of short- and long-range magnetic order in LaCo$_2$P$_2$