This manuscript investigates the performance of downlink broadcasting LoRa networks employing Fountain codes (FCs) and diversity techniques. Specifically, closed-form expressions are derived for the successful packet decoding probability and the cumulative distribution function (CDF) of the number of time slots required to broadcast a message to all end devices (EDs). Simulation results are provided to corroborate the analytical derivations and highlight the impact of key parameters, including the number of gateway transmit antennas, the number of transmitted packets, and the gateway transmit power.