LaCrGe3 has attracted attention as a paradigm example of the avoidance of ferromagnetic (FM) quantum criticality in an itinerant magnet. Here, we combined thermodynamic (specific heat and thermal expansion), transport, x-ray, and neutron scattering as well as μSR measurements to obtain insights on the temperature-pressure phase diagram of LaCrGe3. Consistent with previous studies of the phase diagram by transport measurements, our thermodynamic data shows clearly that the FM transition at TFM changes its character from second order to first order when it is suppressed to low temperatures by pressure. In addition, previous studies demonstrated that for high pressures a new phase occurs below T2, which was proposed to be a long-wavelength antiferromagnetic state (AFMq). In this paper, we provide evidence from our thermodynamic data that this phase transition is preceded by yet another phase transition at T1>T2. Our μSR data indicate that full magnetic volume fraction is only established below T2, but that this magnetism is characterized by a short correlation length. Within the experimental resolution, our neutron-scattering data is not able to identify any magnetic Bragg peaks. Overall, the microscopic magnetic data is therefore consistent with the formation of FM clusters in the proximity of the avoided FM quantum critical point in LaCrGe3. This conclusion is at odds with the previous proposal of AFMq order and raises questions on the role of disorder in this stochiometric compound.