This is something I recall from the 250w low bays that were in the sports hall at my primary school. At switch-on, there would be nothing for a couple of minutes then each lamp would strike one by one within 30 seconds or so. Then each lamp would go out again as above before restriking and running up to full output.
The only others I saw doing the same were the 70w post-tops along the Bournemouth promenade near my Grandparents house. This was all going on back in 1984-5 and I believe these were internal ignitor lamps with the bimetallic snap starters with a heater coil.
What I reckon used to happen is that after the lamp had initially struck, the contacts would cool before the arc tube itself had got hot enough to hold them open. At the second strike, the lamp would gain sufficient heat hence being able to run up fully.
If anyone knows otherwise, please let me know! I know lamp designs have improved over the last 25-30 years so this may explain it all!