Do I have to initialize Dali lamp somehow if I use broadcast commands?
No, the presence or absence of a short address does not affect whether it reacts to broadcast commands. The only legitimate reason to not react to broadcast commands is if the Operating Mode is non zero, so try setting that (to 0) if your controller can send it (added in Edition 2).

Another way you can have this effect is if you controller is sending malformed commands (bit timings, message spacing, encoding) so if you have built that yourself you should check the messages on a scope. It is possible to send messages that are marginal so you are getting inconsistent results. But this shouldn’t be the case for a commercial controller.