Футляр для очков лежит на столе.

Because для normally requires the genitive case.

The noun очки (glasses) is a plural-only noun in Russian, and its genitive plural form is очков.

So:

• очки = glasses
• для очков = for glasses

This whole phrase means a case for glasses.

In Russian, glasses is usually treated as a plural item, just like in English. The basic dictionary form is очки, not a singular form meaning one glass in the sense of eyewear.

So Russian says:

• очки = glasses
• футляр для очков = glasses case / case for glasses

Even if you are talking about one pair of glasses, Russian still uses the plural noun.

На столе is in the prepositional case.

The preposition на can mean different things depending on context:

• на + prepositional = location, meaning on, at
• на + accusative = direction, meaning onto, to

Here the sentence describes location: the case is lying on the table, so Russian uses:

• на столе = on the table

Compare:

• лежит на столе = is lying on the table
• кладёт на стол = puts onto the table

Because after на when talking about location, стол must change to the prepositional form.

The noun changes like this:

• nominative: стол = table
• prepositional: на столе = on the table

So столе is just the correct case form required by the grammar.

Лежит comes from the verb лежать, which means to lie or to be lying.

Russian often uses different verbs depending on the physical position of something:

• лежать = lie, be in a horizontal position
• стоять = stand, be upright
• висеть = hang

So Футляр для очков лежит на столе literally suggests that the glasses case is lying on the table, not standing upright or hanging.

In natural English, we often just say The glasses case is on the table, but Russian is more likely to specify the position.

Because the subject is футляр, which is singular masculine.

• футляр = case
• лежит = is lying

If the subject were plural, the verb would change:

• Футляры лежат на столе. = The cases are lying on the table.

So the verb agrees with the subject in number.

In the present tense, Russian usually does not use a separate word for is / am / are.

So:

• Футляр на столе. = The case is on the table.
• Футляр лежит на столе. = The case is lying on the table.

Russian simply leaves out the present-tense to be in most ordinary sentences.

Для means for.

It shows purpose or intended use:

• футляр для очков = case for glasses
• чашка для чая = cup for tea
• комната для гостей = room for guests

So для очков describes what kind of case it is.

You should think of it as a noun phrase:

• футляр = case
• для очков = for glasses

Together: a glasses case

Grammatically, the main word is футляр, and для очков just describes it. So the verb agrees with футляр, not with очки.

That is why the sentence uses singular лежит, not plural.

Yes. Russian word order is more flexible than English word order, although the neutral order here is very natural:

• Футляр для очков лежит на столе.

You could also say:

• На столе лежит футляр для очков.

This version puts more emphasis on the location first, something like On the table there is a glasses case.

Both are correct, but they may differ slightly in focus.

A few helpful pronunciation points:

• очков: the stress is on the second syllable: очкОв
• лежит: the stress is on the second syllable: лежИт

Also:

• unstressed о is often pronounced more like a in running speech
• ж is like the s in measure
• final consonants in Russian can sound harder than in English

A rough pronunciation guide:

• футляр ≈ foot-LYAR
• для ≈ dlya
• очков ≈ ach-KOF
• лежит ≈ li-ZHEET
• на столе ≈ na sta-LYE

These are only approximations, but they can help at the start.

Yes, you could say:

• Футляр для очков на столе.

This is understandable and can mean The glasses case is on the table.

But лежит is more complete and natural when you want to describe where the object is and its position. Russian often prefers using a positional verb like лежит in this kind of sentence.

Russian nouns have grammatical gender, and футляр is a masculine noun. One clue is that it ends in a consonant, which is a common pattern for masculine nouns.

Because it is masculine singular, any past-tense verbs or adjectives referring to it would match that gender:

• новый футляр = a new case
• футляр лежал на столе = the case was lying on the table

In the present tense, лежит does not show gender, only number.