Operculum lagenae bene claude, ne aqua effundatur.

Because lagenae is genitive singular, meaning of the bottle.

• lagena = bottle
• lagenae = of the bottle

So operculum lagenae means the lid of the bottle.

English often uses of or a noun-noun phrase like bottle lid, but Latin commonly uses the genitive for this relationship.

Operculum is accusative singular.

That is because it is the direct object of claude:

• claude = close!
• What should be closed? operculum = the lid

So the sentence is literally structured as:

• Close the lid of the bottle well

Because claude is an imperative form.

It comes from the verb claudere, meaning to close.
The form claude is the singular present active imperative, used when speaking to one person:

• claude! = close!

If the speaker were commanding more than one person, Latin would use claudite!

Bene is an adverb, meaning well.

It modifies claude:

• bene claude = close well / close it properly

So it tells you how to close the lid.

Here ne means lest or so that ... not.

It introduces a negative purpose clause:

• bene claude, ne aqua effundatur
• close it well, so that the water may not be spilled

In other words, it explains the purpose of closing the lid well.

A very common pattern in Latin is:

• ut
  • subjunctive = so that
• ne
  • subjunctive = so that ... not

Because it is inside a purpose clause introduced by ne.

Latin normally uses the subjunctive after ut or ne when expressing purpose:

• ne aqua effundatur = so that the water may not be poured out / spilled

So the subjunctive is not random; it is required by the grammar of the clause.

Effundatur is:

• present
• subjunctive
• passive
• 3rd person singular

from effundere, meaning to pour out, to spill, or to let flow out.

So:

• effundatur = may be poured out, may be spilled

Since aqua is singular, the verb is also singular.

Because the sentence focuses on the water as the thing that might come out:

• aqua effundatur = the water may be spilled / poured out

The passive is very natural here in Latin. English often says the water spills or the water is spilled, depending on style, but Latin chooses the passive form to make aqua the grammatical subject.

Because aqua is the subject of effundatur.

In the clause ne aqua effundatur:

• aqua = the water
• effundatur = may be spilled

Since the water is the subject of that verb, it appears in the nominative case.

Yes. That is a very literal translation.

A smoother English translation might be:

• Close the bottle’s lid well, so that the water does not spill
• Close the lid tightly so the water won’t spill

But grammatically, ne often corresponds very closely to lest in older or more literal English.

Latin word order is more flexible than English because the endings show the grammatical relationships.

So Latin can say:

• Operculum lagenae bene claude, ne aqua effundatur

without needing a fixed English-like order.

A few stylistic points:

• operculum lagenae puts the object first
• bene stands near the verb it modifies
• the purpose clause comes after the main command

English relies more on word order; Latin relies more on case endings and verb forms.

Yes, that would also be possible.

Both mean the lid of the bottle. Latin often allows either:

• operculum lagenae
• lagenae operculum

The difference is mainly one of style or emphasis, not basic grammar. In this sentence, operculum lagenae is a perfectly normal order.

Yes: operculum is a neuter second-declension noun.

That means forms like:

• operculum = nominative singular or accusative singular
• here it is accusative singular because it is the direct object

Neuter nouns have the rule:

• nominative singular and accusative singular are the same

So a learner might notice that operculum looks the same in both cases; you determine its role from the sentence.

Because those forms do different jobs:

• claudere = to close (infinitive)
• claudit = he/she/it closes (indicative statement)
• claude = close! (command)

Since the sentence gives an order, Latin uses the imperative: claude.

Normally, classical Latin uses ne for negative purpose:

• ne aqua effundatur = so that the water may not be spilled

While ut non can appear in some contexts, for straightforward negative purpose, ne is the standard and expected choice. So in this sentence, ne is exactly what a learner should expect.