This paper investigates the ground state energy of a bound quantum system consisting of three particles (trimer) in the Lennard-Jones potential. Two stochastic methods were applied: the variational Monte Carlo (VMC) and the diffusion Monte Carlo (DMC) algorithms. The VMC simulation yielded stable results and estimated the upper bound of the system’s ground state energy, with optimal parameters for the trial correlation function being determined for examples of two potentials. By applying the DMC algorithm, the system reached a lower energy state, but with somewhat larger fluctuations in average quantities compared to the VMC simulation, indicating potential technical or theoretical challenges. The dependence of the energy simulated by the DMC algorithm on the imaginary time step was studied, and the true ground state of the system was estimated. Possible causes include inadequately chosen parameters, difficulties in controlling energy fluctuations and walker numbers, or technical issues in the code. Using the results from VMC, the universality of the relation between energy and size of trimers in 2D has been investigated. In conclusion, to obtain a more accurate estimate of the trimer’s ground state, it is necessary to increase the computational power, expand the VMC simulation to cover a broader range of parameters, and improve the DMC algorithm by adding pure estimators.