Lass bitte das Glas auf dem Tisch stehen.

Lass is the informal singular imperative of lassen, used when speaking to one person you would call du.

So:

• lass = command to one person (du)
• lasst = command to more than one person (ihr)
• lassen Sie = formal command

Examples:

• Lass bitte das Glas auf dem Tisch stehen. = speaking to one person informally
• Lasst bitte das Glas auf dem Tisch stehen. = speaking to several people
• Lassen Sie bitte das Glas auf dem Tisch stehen. = formal

German imperatives usually do not include the subject pronoun unless you want special emphasis.

Here stehen lassen means to leave something where it is or not move/remove it.

Literally, the parts are:

• stehen = to stand
• lassen = to let, allow, leave

Together, etwas stehen lassen often means:

• leave it there
• don’t take it away
• don’t move it

So in this sentence, the idea is not just that the glass is standing, but that the speaker wants it to remain on the table.

Because lassen is the conjugated verb, and stehen stays in the infinitive at the end.

This is a very common German pattern:

• conjugated verb earlier in the clause
• second verb in infinitive form at the end

Examples:

• Ich lasse das Fenster offen.
• Lass das Glas auf dem Tisch stehen.
• Er lässt sein Fahrrad draußen stehen.

So lass is the command form, and stehen completes the meaning at the end.

Because das Glas is the direct object of lassen, so it is in the accusative case.

The noun Glas is neuter:

• nominative: das Glas
• accusative: das Glas
• dative: dem Glas

In this sentence, you are leaving the glass, so it is the thing affected by the action:

• Lass das Glas ... stehen.

Because neuter nominative and accusative look the same, the form stays das Glas.

Because auf is a two-way preposition, and German chooses the case based on whether the phrase shows:

• location → dative
• movement toward a destination → accusative

Here the glass is already on the table, and the speaker wants it to stay there. That is location, so German uses dative:

• auf dem Tisch = on the table

Compare:

• Stell das Glas auf den Tisch. = Put the glass onto the table.
  (movement to a destination → accusative)
• Das Glas steht auf dem Tisch. = The glass is on the table.
  (location → dative)
• Lass das Glas auf dem Tisch stehen. = Leave the glass on the table.
  (location → dative)

German often uses verbs that describe the position of an object more specifically than English does.

Common ones are:

• stehen = stand
• liegen = lie
• hängen = hang

A glass, bottle, or cup is often thought of as standing upright, so German naturally says:

• Das Glas steht auf dem Tisch.

English usually prefers:

• The glass is on the table.

So this is a normal difference between the two languages, not something strange or poetic.

Usually, no—at least not in careful standard German.

Lassen normally needs something to complete the idea here. Without stehen, the sentence feels unfinished.
The full sentence Lass bitte das Glas auf dem Tisch stehen clearly means leave the glass on the table.

If you remove stehen, listeners may wonder what exactly you mean:

• leave it there?
• put it there?
• let it be there?

So stehen is important for the intended meaning.

Bitte is fairly flexible in German.

All of these are possible:

• Lass bitte das Glas auf dem Tisch stehen.
• Bitte lass das Glas auf dem Tisch stehen.
• Lass das Glas bitte auf dem Tisch stehen.

They all mean roughly the same thing: Please leave the glass on the table.

The version in your sentence sounds very natural and neutral.

The choice depends on how German imagines the object’s position.

• stehen lassen = leave something standing/upright
• liegen lassen = leave something lying

Examples:

• Lass bitte das Glas auf dem Tisch stehen.
  A glass is upright, so it steht.
• Lass bitte das Buch auf dem Tisch liegen.
  A book usually lies flat, so it liegt.

This is one of those areas where German is more physically specific than English.

Grammatically, it is an imperative, so it is a command form.
But because it includes bitte, it sounds like a polite request rather than a harsh order.

Compare:

• Lass das Glas auf dem Tisch stehen. = stronger, more direct
• Lass bitte das Glas auf dem Tisch stehen. = softer, more polite

So it is structurally a command, but in real use it often functions as a request.