Аромат лилии сильнее, чем аромат ромашки.

They are both in the genitive case because they depend on аромат and mean of ...:

• аромат лилии = the aroma of the lily
• аромат ромашки = the aroma of the chamomile/daisy

So the basic pattern is:

• аромат + genitive

Examples:

• аромат розы = aroma of a rose
• аромат кофе = aroma of coffee
• аромат цветка = aroma of a flower

In this sentence:

• лилия → лилии (genitive singular)
• ромашка → ромашки (genitive singular)

The dictionary form is лилия. But after аромат, you need the genitive singular.

For feminine nouns ending in -ия, the genitive singular usually ends in -ии:

• лилия → лилии
• Мария → Марии
• история → истории

So аромат лилии literally means aroma of the lily.

For most feminine nouns ending in -а, the genitive singular changes to -ы or -и.

• ромашка → ромашки

Normally you might expect -ы, but after certain consonants, Russian uses -и instead. Since ромашка ends with к, the genitive is ромашки, not ромашкы.

So:

• ромашка = chamomile/daisy
• аромат ромашки = aroma of chamomile/daisy

Сильнее is the comparative form of сильный (strong).

• сильный = strong
• сильнее = stronger

So:

• Аромат лилии сильнее = The aroma of the lily is stronger

Russian often forms comparatives with -ее / -ей:

• быстрый → быстрее = faster
• интересный → интереснее = more interesting
• сильный → сильнее = stronger

So the sentence is comparing two aromas.

In Russian, the verb to be is usually omitted in the present tense.

So where English says:

• The aroma of the lily is stronger

Russian simply says:

• Аромат лилии сильнее

There is no present-tense есть here. Using есть would sound wrong in this sentence.

This is very normal in Russian:

• Он дома = He is at home
• Она умная = She is smart
• Книга интересная = The book is interesting

Чем means than in comparisons.

So:

• сильнее, чем ... = stronger than ...

In your sentence:

• Аромат лилии сильнее, чем аромат ромашки.
• The aroma of the lily is stronger than the aroma of chamomile/daisy.

This is one of the most common comparison patterns in Russian:

• Он выше, чем я. = He is taller than me.
• Этот фильм интереснее, чем тот. = This film is more interesting than that one.

Yes. You could say:

• Аромат лилии сильнее, чем ромашки.

This is understandable, because аромат is implied after чем.

But the full version:

• Аромат лилии сильнее, чем аромат ромашки.

is clearer and more explicit, especially for learners or in more careful style.

So both are possible:

• full: ...чем аромат ромашки
• shorter: ...чем ромашки

Yes, Russian word order is fairly flexible, but the original order is the most neutral:

• Аромат лилии сильнее, чем аромат ромашки.

This sounds natural and straightforward.

You could rearrange parts for emphasis, for example:

• Сильнее аромат лилии, чем аромат ромашки.
• Чем аромат ромашки, аромат лилии сильнее.

But these sound more marked or literary, and they are not the usual way a learner should say it.

So the best default pattern is:

• [thing 1] + comparative + чем + [thing 2]

Not exactly.

• аромат usually suggests a pleasant, fragrant smell
• запах is the general word for smell/odor, whether pleasant, neutral, or unpleasant

So:

• аромат лилии sounds elegant and positive: the fragrance/aroma of a lily
• запах лилии is possible, but more neutral

Compare:

• приятный аромат = pleasant fragrance
• неприятный запах = unpleasant smell

So аромат is a very suitable choice for flowers.

A helpful stress guide is:

• Арома́т ли́лии си́льнее, чем арома́т рома́шки.

Approximate pronunciation:

• a-ra-MAT LEE-lee-ee SEEL-nee-ye, chem a-ra-MAT ra-MASH-kee

A few notes:

• чем sounds like chem
• сильнее has the stress on the first syllable: си́льнее
• лилии has several vowels in a row, so say it clearly: ли́-ли-и

It can refer to a daisy-like flower, and in many learning contexts it is translated as chamomile. The exact English choice depends on context.

So аромат ромашки may be rendered as:

• the aroma of chamomile
• the scent of a daisy/chamomile-like flower

In many basic Russian-learning examples, ромашка is often taught as chamomile.

Russian has no articles, so the sentence itself does not explicitly mark a, the, or zero article.

So depending on context, this could mean:

• The aroma of the lily is stronger than the aroma of the chamomile
• A lily’s aroma is stronger than a chamomile’s
• The aroma of lilies is stronger than that of chamomile
  though the singular wording most directly suggests one flower/type at a time

Usually, you choose the best English article from context, because Russian does not show it directly.