The revolution of the solid-state lighting technology and the looming radio frequency (RF) spectrum crisis enabled the rapid evolution of visible light communication (VLC) in the recent times. To furnish contemporaneous illumination and communication, VLC relies on white light emitting diodes (WLEDs). However, the limited modulation bandwidth of WLEDs poses a threat to VLC as the achievable data rates are drastically minimized. Eventually, to enhance the achievable throughput, the pre-eminent way is to apply orthogonal frequency division multiplexing (OFDM) to a VLC system. Furthermore, a VLC system can also exploit non-orthogonal multiple access (NOMA) scheme to bestow with seamless services to the multiple users. However, much similar to the RF-based OFDM system, the OFDM-VLC system also inherits one of the serious disadvantages like the high peak to average power ratio (PAPR). In addition, the rapid fluctuations of the continuous time-domain signal amplitude in DC-biased optical OFDM (DCO-OFDM) results in much complicated design of the LED driver circuitry for driving the LED. Thus, to overcome such drawbacks, we incorporate delta-sigma modulators (DSM) to the NOMA-VLC system which is making use of DCO-OFDM, and we analyze its performance over VLC channel environment. The stunning advantage imparted by the proposed DSM-based DCO-OFDM-NOMA-VLC system is that the continuous amplitude of the time-domain transmitted signal is converted into two levels for driving the LED. Additionally, with the major goal to maximize the sum throughput of the proposed multiuser VLC system by taking into consideration both the user fairness as well as the intensity constraints, we derived the optimal values for the power allocation coefficients corresponding to the fair power allocation algorithm. Furthermore, the dynamically varying fair power allocation algorithm is compared with the fixed/static power allocation algorithm. The major contribution of this work is of two-fold: firstly, the proposed DCO-OFDM-NOMA-VLC system which is making use of DSM exhibits a remarkable reduction in PAPR when compared with the conventional system without the application of DSM, where the proposed system demonstrates a significant gain of 4.78 dB in terms of PAPR reduction. Secondly, from the simulated results it can affirmed that the proposed system not only achieves enhanced sum rates and better outage performance but also imparts a better bit error ratio (BER) performance corresponding to the far user.