In VVC draft 8, low-frequency non-separable transform (LFNST) is always disabled for chroma components when single-tree partition is applied, and applied to both luam and chroma components in dual-tree parition. However, it was found that the current LFNST signalling of luma component in single-tree is still conditioned on 1) chroma transform skip flags and 2) the positions of last non-zero coefficients of chroma components. In this contribution, two aspects are proposed to simplify the existing LFNST signaling design in VVC draft 8. In the first aspect, it is proposed to remove the signalling dependency of the luma LFNST on the chroma components in single-tree partition for a cleaner design. In the second aspect, it is proposed to disable the LFNST for chroma components in dual-tree partition. Simulation results show that the first aspect leads to negligible impact on coding efficiency.