Both of you are right.
Radical reactions start by initiation step, go on by propagation step and finally finish by termination step.
Initiation step with chlorine alone, starts by thermal degradation of the chlorine atom to chlorine radicals.
Cl-Cl → 2 Cl·
In contrast to the thermal degradation of Et4Pb to ethyl radicals that is the initiation step in that case and which has a lower activation energy and therefore, it occurs at lower temperature.
CH3CH2Pb(CH3CH2)3 → CH3CH2· + ·Pb(CH3CH2)3 →→ 4 CH3CH2· + Pb4.
Pb4. + 2 Cl-Cl → PbCl4
CH3CH2· + Cl-Cl → CH3CH2Cl + Cl·
PS: So this in turn increases the concentration of Cl· at a lower temperature? (it’s more descriptive.)