La nuclear magnetic resonance (NMR) measurements under pressure ($p = 0-2.64$ GPa) have been carried out to investigate the static and dynamic magnetic properties of the itinerant ferromagnet LaCrGe. La-NMR spectra for all measured pressures in the ferromagnetically ordered state show a large shift due to the internal field induction 4 T at the La site produced by Cr ordered moments. The change in by less than 5% with up to 2.64~GPa indicates that the Cr 3 moments are robust under pressure. The temperature dependence of NMR shift and $B_{\rm int}\sim$ 50~K under higher pressures in a magnetic field of 7.2 T. Based on the analysis of NMR data using the self-consistent-renormalization (SCR) theory, the spin fluctuations in the paramagnetic state well above are revealed to be three dimensional ferromagnetic throughout the measured region.

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