Background: Velocity loss (VL) at 1 m·s−1 can help to determine neuromuscular fatigue after performing an exercise protocol. The aim of this study was to analyse muscle fatigue and metabolic stress during the 15 min that follow the execution of a bench press (BP) exercise protocol. Methods: Forty-four healthy male students of sports science performed two exercise sessions separated by one week of rest. In the first week, the participants carried out a test with progressive loads in the (BP) exercise until reaching the one-repetition maximum (1RM) in order to obtain the load–velocity relationship of each participant. In the second week, each participant conducted three BP exercise sets at an intensity of 70% of 1RM, determining this load through the mean propulsive velocity (MPV) obtained from the individual load–velocity relationship, with the participants performing the maximum number of repetitions (MNR) to muscle failure. Two minutes of rest were allocated between sets. MPV at 1 m·s−1 and blood lactate concentrations were recorded before executing the exercise and at minute 0, 5, 10 and 15 after performing the exercise protocol. Results: A two-factor repeated measures ANOVA was performed. MPV at 1 m·s−1 in minute 0 post-exercise was −33.3% (p < 0.05), whereas in minute 10 and 15 post-exercise, it was ≈−9% (p > 0.05). Regarding the blood lactate levels, significant differences were observed in all measurements before and after the exercise protocol (p < 0.001), obtaining ≈7 mmol·L−1 at minute 10 post-exercise and 4.3 mmol·L−1 after 15 min of recovery. Conclusions: MPV with medium or moderate loads shows a certain recovery from minute 10 of rest. However, the blood lactate levels are still high (>5 mmol·L−1). Therefore, although there seem to be certain conditions to reach a similar maximum MPV peak, the residual fatigue at the neuromuscular level and the non-recovery of metabolic homeostasis would hinder the reproduction of these protocols, both at the level of applied stimulus and from a methodological perspective, since a long recovery time would be required between sets and exercises.