The integration of wireless communication, e.g., in real- or quasi-real-time applications, is related to many challenges such as energy consumption, communication range, quality of service, and reliability. The improvement of wireless sensor networks (WSN) performance starts by enhancing the capabilities of each sensor node. To minimize latencies without increasing energy consumption, wake-up receiver (WuRx) nodes have been introduced in recent works since they can be always-on or power-gated with short latencies by a power consumption in the range of some microwatts. Compared to standard receiver technologies, they are usually characterized by drawbacks in terms of sensitivity. To overcome the limitation of the sensitivity of WuRxs, a design of a low noise amplifier (LNA) with several design specifications is required. The challenging task of the LNA design is to provide equitable trade-off performances such as gain, power consumption, the noise figure, stability, linearity, and impedance matching. The design of fast settling LNA for a duty-cycled WuRx front-end operating at a 868 MHz frequency band is investigated in this work. The paper details the trade-offs between design challenges and illustrates practical considerations for the simulation and implementation of a radio frequency (RF) circuit. The implemented LNA competes with many commercialized designs where it reaches single-stage 12 dB gain at a 1.8 V voltage supply and consumes only a 1.6 mA current. The obtained results could be made tunable by working with off-the-shelf components for different wake-up based application exigencies.