Линза лежит рядом с футляром для очков.

Because the expression рядом с means next to / beside and requires the instrumental case.

• dictionary form: футляр
• instrumental singular: футляром

So:

• рядом с футляром = next to the case

This is a very common pattern:

• рядом с домом = next to the house
• рядом с машиной = next to the car

Without the case change, the phrase would be ungrammatical.

Because для means for and is followed by the genitive case.

The noun очки means glasses and is normally used only in the plural. Its forms are:

• nominative: очки
• genitive: очков

So:

• футляр для очков = a case for glasses

This is the same pattern as:

• бутылка для воды = bottle for water
• сумка для книг = bag for books

Russian often uses different verbs for the physical position of an object, where English would simply use is.

Here, лежит comes from лежать, meaning to lie. It is used for something that is positioned horizontally or simply resting somewhere.

So:

• Линза лежит... = The lens is lying... / The lens is...

Russian commonly distinguishes between:

• лежать = lie
• стоять = stand
• висеть = hang

For a lens, лежит sounds natural because a small object like that is typically thought of as lying on a surface.

Линза can mean lens in a general sense. Depending on context, it may refer to:

• a contact lens
• a glasses lens
• a camera lens component
• an optical lens in general

In this sentence, because it is near a case for glasses, a learner might first think of a glasses lens. But the word itself is not limited to that meaning.

If Russian wants to be more specific, it can say:

• контактная линза = contact lens
• линза очков = a glasses lens

Рядом с means next to, beside, or close to something.

When you name the thing that something is near, you normally use:

• рядом с + instrumental

Example:

• рядом с футляром = next to the case

Yes, рядом can also be used by itself as an adverb meaning nearby:

• Линза лежит рядом. = The lens is nearby.

So:

• рядом = nearby
• рядом с чем-то = next to something

Yes, you could, but the nuance is a little different.

• рядом с футляром = right next to / beside the case
• около футляра = near the case

Рядом с usually suggests closer physical proximity, often almost touching or very near.
Около is a bit broader and can simply mean near.

Also note the grammar difference:

• рядом с + instrumental
• около + genitive

So:

• рядом с футляром
• около футляра

Both are grammatical, but they are not always identical in feel.

Yes, Russian word order is flexible. This sentence uses a very neutral, natural order:

• Линза = subject
• лежит = verb
• рядом с футляром = location

You can change the order for emphasis or context:

• Рядом с футляром лежит линза. = Next to the case lies a lens.
• Лежит линза рядом с футляром. = possible, but more marked and context-dependent

Even when the order changes, the case endings help show the grammatical relationships.

Russian does not have articles like English a/an and the.

So линза can mean:

• a lens
• the lens

and футляром can mean:

• a case
• the case

Which one is intended depends on context. In real communication, the listener usually understands from the situation whether the object is specific or not.

Лежит is the 3rd person singular present tense form of лежать.

That means it matches a singular subject such as линза.

Conjugation of лежать in the present tense:

• я лежу = I lie
• ты лежишь = you lie
• он / она лежит = he / she / it lies
• мы лежим = we lie
• вы лежите = you lie
• они лежат = they lie

Since линза is singular, Russian uses лежит.

Yes, it is a very normal and standard way to say glasses case.

Literally it is:

• футляр = case
• для очков = for glasses

Russian often forms this kind of expression with для rather than by stacking nouns the way English does.

Compare:

• case for glasses in Russian structure
• glasses case in English structure

So even though English uses one noun before another, Russian often prefers a phrase like X for Y.

The main stresses are:

• ЛИнза
• леЖИТ
• РЯдом
• футЛЯром
• очКОВ

A rough pronunciation guide:

• Линза = LEEN-zuh
• лежит = lye-ZHEET
• рядом = RYA-dum
• с футляром = s foot-LYA-rum
• для очков = dlya ach-KOF

A careful full reading would sound roughly like:

ЛИ-нза ле-ЖИТ РЯ-дом с фут-ЛЯ-ром для оч-КОВ.

Yes. Линза means lens, so it refers to just one lens, not the whole glasses.

If you mean the glasses themselves, you would use:

• очки = glasses

For example:

• Очки лежат рядом с футляром. = The glasses are lying next to the case.

That would also change the verb form, because очки is plural:

• очки лежат
• not очки лежит