Why 'quizás' can take the subjunctive but 'a lo mejor' doesn't
Spanish has a whole family of ways to say 'maybe': quizás, tal vez, a lo mejor, puede que and a few more. They all mean roughly the same thing, but they do not all take the same verb mood. Some can be followed by the indicative or the subjunctive, one almost always takes the indicative, and one only takes the subjunctive.
English speakers trip over this because English 'maybe' never changes the verb: 'maybe he knows' is just 'maybe he knows'. In Spanish, the word you choose for 'maybe' decides which verb form comes next. With some of these words, your choice of mood also shows how doubtful you are.
Think of these words as falling into three groups:
quizás, quizá, tal vez and probablemente take either mood. The subjunctive sounds more doubtful, and the indicative sounds more confident.
a lo mejor (and capaz in Latin America) normally takes the indicative, even though the meaning is just as uncertain.
puede que is really a verb phrase, 'it may be that', and the que clause after it always needs the subjunctive.
For the flexible words, compare these two sentences. The first sounds like a real doubt. The second sounds closer to 'I think you're probably right'.
Tal vez, quizás and quizá are interchangeable. Quizá is simply a slightly more formal spelling of quizás. All three are used everywhere in the Spanish-speaking world.
Probablemente means 'probably', so it usually sounds fairly confident and mostly takes the indicative. The subjunctive is still possible when you want to sound less sure. Posiblemente and seguramente, when it means 'probably', work the same way.
A lo mejor is very common in everyday speech, especially in Spain. It takes the indicative, even when the speaker has no idea whether something is true. In much of Latin America, capaz or capaz que plays the same role in casual speech and is also mostly followed by the indicative.
After puede que, the subjunctive is required. Saying puede que viene is a clear mistake.
Acaso means 'perhaps' in literary statements, where it usually takes the subjunctive. In everyday Spanish, though, you mostly hear it in questions that express surprise or reproach, and there it takes the indicative.
The subjunctive is only possible when quizás, tal vez or probablemente comes before the verb. If you add the word at the end as an afterthought, the verb stays in the indicative.
The typical mistake is to treat all these words alike. Learners who have just discovered the subjunctive often say a lo mejor esté, which sounds wrong to most native speakers. Others forget the subjunctive after puede que. If you're unsure, pair a lo mejor with the indicative and puede que with the subjunctive, and use quizás or tal vez when you want the freedom to choose.
Finally, don't confuse these words with ojalá. It also always takes the subjunctive, but it expresses a wish ('I hope'), not a possibility.
To say 'maybe' in Spanish, remember three groups. A lo mejor (and Latin American capaz) takes the indicative. Puede que always takes the subjunctive. Quizás, quizá, tal vez and probablemente take either mood when they come before the verb: use the subjunctive to sound more doubtful and the indicative to sound more confident.