In order to elucidate features of low-temperature structural phase transitions in La1.5Sr0.1Nd0.4CuO4, in-situ observation was performed by transmission electron microscopy. A series of dark field images using the 100 forbidden spot reveal that there are two types of sites for the nucleation of the LTO/LTT phase; that is, the twin boundary between neighboring LTO I domains and the interior of the domain. When the temperature is lowered from the LTO I phase, the LTO/LTT phase is first nucleated along the twin boundary around 120 K and exhibits a lateral growth, which is relatively suppressed. As a result of the suppression, the LTO/LTT region nucleated along the boundary is never extended in a whole area. On further cooling to 12 K, the LTO/LTT phase with a spotty-shape also appears in the interior of the LTO I domain. The most interesting feature of the spotty-shape phase is that on aging at 12 K some LTO/LTT regions nucleated inside the domain are annihilated and then appear again. That is, the growth of the LTO/LTT phase in the interior of the domain exhibits a very unique behavior. The present data suggest that the unique behavior originates from the interaction between the order parameter and the spontaneous strain accompanied by the transition.