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Context.Sources that leak Lyman continuum (LyC) photons and lead to the reionisation of the universe are an object of intense study using multiple observing facilities. Recently, the Low-redshift LyC Survey (LzLCS) has presented the first large sample of LyC emitting galaxies at low redshift (z ∼ 0.3) with theHubbleSpace Telescope Cosmic Origins Spectrograph. The LzLCS sample contains a robust estimate of the LyC escape fraction (f_esc^LyC) for 66 galaxies, spanning a wide range off_esc^LyCvalues. Aims.Here, we aim to study the dependence off_esc^LyCon the radio continuum (RC) properties of LzLCS sources. Overall, RC emission can provide unique insights into the role of supernova feedback, cosmic rays (CRs), and magnetic fields from its non-thermal emission component. RC emission is also a dust-free tracer of the star formation rate (SFR) in galaxies. Methods.In this study, we present Karl G. Jansky Very Large Array (VLA) RC observations of the LzLCS sources at gigahertz (GHz) frequencies. We performed VLAC(4−8 GHz) andS(2−4 GHz) band observations for a sample of 53 LzLCS sources. We also observed a sub-sample of 17 LzLCS sources in theL(1−2 GHz) band. We detected RC from bothC- andS-bands in 24 sources for which we are able to estimate their radio spectral index across 3−6 GHz, denoted asα_6 GHz^3 GHz. We also used the RC luminosity to estimate their SFRs. Results.The radio spectral index of LzLCS sources spans a wide range, from flat (≥ − 0.1) to very steep (≤ − 1.0). They have a steeper meanα_6 GHz^3 GHz(≈ − 0.92) compared to that expected for normal star-forming galaxies (α_6 GHz^3 GHz ≈ −0.64). They also show a larger scatter inα_6 GHz^3 GHz(∼0.71) compared to that of normal star-forming galaxies (∼0.15). The strongest leakers in our sample show flatα_6 GHz^3 GHz, weak leakers haveα_6 GHz^3 GHzclose to normal star-forming galaxies and non-leakers are characterized by steepα_6 GHz^3 GHz. We argue that a combination of young ages, free-free absorption, and a flat cosmic-ray energy spectrum can altogether lead to a flatα_6 GHz^3 GHzfor strong leakers. Non-leakers are characterized by steep spectra which can arise due to break or cutoff at high frequencies. Such a cutoff in the spectrum can arise in a single injection model of CRs characteristic of galaxies which have recently stopped star-formation. The dependence off_esc^LyConα_6 GHz^3 GHz(which is orientation-independent) suggests that the escape of LyC photons is not highly direction-dependent at least to the first order. The radio-based SFRs (SFR^RC) of LzLCS sources show a large offset (∼0.59 dex) from the standard SFR^RCcalibration. We find that addingα_6 GHz^3 GHzas a second parameter helps us to calibrate the SFR^RCwith SFR_UVand SFR_Hβwithin a scatter of ∼0.21 dex. Conclusions.For the first time, we have found a relation betweenα_6 GHz^3 GHzandf_esc^LyC. This hints at the interesting role of supernovae feedback, CRs, and magnetic fields in facilitating the escape (alternatively, and/or the lack) of LyC photons.