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This paper focuses on a lossy transmission of binary symmetric source (BSS) with down-link non-orthogonal multiple access (DL-NOMA). The transmitted binary sequences are lossy-compressed descriptions of the same BSS, which are overlapped in a specified signal format, corresponding to the receivers with pre-determined distortion requirements. Despite a higher spectrum efficiency achieved by DL-NOMA, redundancy may still remain if the overlapped descriptions are correlated. In this work, a system combining DL-NOMA and successive refinement, referred to as DN-SR, is proposed. Specifically, instead of re-constructing the source by a single description, the receiver can achieve a low distortion by first recovering the basic description, and then refining it with the help of another refinement description. If the two descriptions are made independent, transmission efficiency of the conventional DL-NOMA can be further improved. As the main contribution, this paper derives the outage probability of DN-SR in closedform, assuming block Rayleigh fading channels. The advantage of DN-SR is numerically studied in terms of the system outage probability, compared to both the conventional DL-NOMA, and a modified DL-NOMA which exploits the correlation between descriptions, referred to as DN-CE. Finally, the optimal power allocation to the two descriptions is investigated for DN-SR, aiming to minimize the system outage probability.