Does Red Light Therapy Speed Up Recovery?

The simple answer is yes. Low Level Light Therapy (either through LASERs or Light Emitting Diodes - LEDs) has been scientifically shown to speed up recovery after sports, as well as after injuries, increasing return-to-play.
In a trial with volleyball players, Low Level Laser therapy decreased post-exercise levels of blood lactate, creatine kinase (widely as an index of skeletal muscle fiber damage in sport and exercise), and C-reactive protein (strenuous exercise can induce a transient increase of CRP) (Leal Junior et al., 2010).
Low Level Laser therapy has also been shown to decrease muscle fatigue (Gorgey et al., 2008; de Almeida et al, 2012) and the activities of lactate dehydrogenase and Creatine Kinase (markers of tissue damage), as well as reduce oxidative stress.
Low level light therapy with red and infrared emitting diodes has also shown positive effects on delayed onset muscle soreness and an increase in muscle performance (Vinck et al., 2006); as well as a significant reduction of CK levels, lactate and c-reactive protein (CRP) in blood after exercise (Leal et al., 2009; 2009-B).
Moreover, red and infrared light therapy significantly and safely reduced the return-to-play in injured university athletes over a wide range of injuries with no adverse events (Foley at al.  2016); as well as significantly increased the time of staying in the pitch and improved all the biochemical markers evaluated in futsal players (De Marchi et al., 2018).
Lastly, it is worth mentioning that red and infrared low level light therapy has been proven to be more effective than cryotherapy at reducing recovery time and decreasing delayed onset muscle soreness after strenuous exercise (Fisher et al., 2019).
de Almeida P, Lopes-Martins RA, De Marchi T, Tomazoni SS, Albertini R, Corrêa JC, Rossi RP, Machado GP, da Silva DP, Bjordal JM, Leal EC., Jr Red (660 nm) and infrared (830 nm) low-level laser therapy in skeletal muscle fatigue in humans: what is better ? Lasers Med Sci. 2012;27(2):453–8.
De Marchi T, Leal EC, Junior, Bortoli C, Tomazoni SS, Lopes-Martins RA, Salvador M. Low-level laser therapy (LLLT) in human progressive-intensity running: effects on exercise performance, skeletal muscle status, and oxidative stress. Lasers Med Sci. 2012;27(1):231–6.
De Marchi T, Leal-Junior ECP, Lando KC, Cimadon F, Vanin AA, da Rosa DP, Salvador M. Photobiomodulation therapy before futsal matches improves the staying time of athletes in the court and accelerates post-exercise recovery. Lasers Med Sci. 2019 Feb;34(1):139-148. doi: 10.1007/s10103-018-2643-1. Epub 2018 Sep 27. PMID: 30264178.
Fisher SR, Rigby JH, Mettler JA, McCurdy KW. The Effectiveness of Photobiomodulation Therapy Versus Cryotherapy for Skeletal Muscle Recovery: A Critically Appraised Topic. J Sport Rehabil. 2019 Jul 1;28(5):526-531. doi: 10.1123/jsr.2017-0359. Epub 2019 Jan 29. PMID: 29952693.
Foley J, Vasily DB, Bradle J, Rudio C, Calderhead RG. 830 nm light-emitting diode (led) phototherapy significantly reduced return-to-play in injured university athletes: a pilot study. Laser Ther. 2016 Mar 31;25(1):35-42. doi: 10.5978/islsm.16-OR-03. PMID: 27141153; PMCID: PMC4846838.
Gorgey AS, Wadee AN, Sobhi NN. The effect of low-level laser therapy on electrically induced muscle fatigue: a pilot study. Photomed Laser Surg. 2008;26(5):501–6.
Leal EC, Junior, Lopes-Martins RA, Baroni BM, De Marchi T, Rossi RP, Grosselli D, Generosi RA, de Godoi V, Basso M, Mancalossi JL, Bjordal JM. Comparison between single-diode low-level laser therapy (LLLT) and LED multi-diode (cluster) therapy (LEDT) applications before high-intensity exercise. Photomed Laser Surg. 2009;27(4):617–23.
Leal EC, Junior, Lopes-Martins RA, Rossi RP, De Marchi T, Baroni BM, de Godoi V, Marcos RL, Ramos L, Bjordal JM. Effect of cluster multi-diode light emitting diode therapy (LEDT) on exercise-induced skeletal muscle fatigue and skeletal muscle recovery in humans. Lasers Surg Med. 2009-B;41(8):572–7.