I've been running Michelin radial tubes in LT21585-16 Michelin-manufactured tires for 20+ years, 40K miles, no problem other than the odd flat. These were recommended by the Michelin tire dealer that installed the tires on the stock 1952 rims. You do have to use tubes that are intended for use with radial tires
Those must have been tube type radial tires, Michelin does not reccomend tubes in their tubless tires.
BTW, I've been in the tire business for 20 years, mainly dealing with Michelin and Goodyear tires.
