Chaotic: Inimical to civilization and social organization. Incapable of following orders and unlikely to put the needs of others (especially groups / nations) ahead of their own. Chaotic is the alignment of demons, Faerie, many mages, and all serial killers.
Lawful: The philosophical stance that civilization, regardless of how it is organized, is preferable to other alternatives. Will always privilege group processes and consensual decision making over rogue action. Lawful is the alignment of unicorns, devils, army personnel, most clerics, and all social workers.
Neutral: Neither fully committed to Law nor to Chaos; pragmatic. Many inflections are possible here: the Neutral character may be apathetic, invested in balance, leaning toward lawfulness, leaning toward chaos, or none of the above.
Neutral characters with lawful tendencies work well in groups, and will typically follow the orders of Lawful characters or characters whose ideas seem reasonably certain to benefit the group. Neutral characters who prefer Chaos have very little discipline, and only trust their own authority. They can work cooperatively but often undermine outside authority and resist falling in line with group decisions too easily.
Neutral is the alignment of the vast majority of dungeon delvers and adventurers.
Doublechecking yesterday morning to make sure I haven't been playing wrong for a quarter of a century, I did confirm that OD&D, Holmes Basic, Mentzer Basic, AD&D, OSRIC, and Swords & Wizardry do not have this "one try only" language in the rules for secret doors.
I'm truly flabbergasted that a game that so features exploration as a primary activity would have such a limitation. To me, secret doors are time sinks, and if a party wants to take the time to make an extra check (or five) at the cost of a turn each, running down their light sources and risking wandering monsters, that's great!
House Rules available as pdf here.
See also this post about the Arandish Entourage Approach to Retainers.