Square-shaped or rectangular nanoparticles (NPs) of lanthanum oxide (LaOx) were synthesized and layered by convective self-assembly to demonstrate an analog memristive device in this study. Along with non-volatile analog memory effect, selection diode property could be coexistent without any implementation of heterogeneous multiple stacks with similar to 1 mu m thick LaOx NPs layer. Current-voltage (I-V) behavior of the LaOx NPs resistive switching (RS) device has shown an evolved current level with memristive behavior and additional rectification functionality with threshold voltage. The concurrent memristor and diode type selector characteristics were examined with electrical stimuli or spikes for the duration of 10-50 ms pulse biases. The pulsed spike increased current levels at a read voltage of +0.2 V sequentially along with +/- 7 V biases, which have emulated neuromorphic operation of long-term potentiation (LTP). This study can open a new application of rare-earth LaOx NPs as a component of neuromorphic synaptic device.