Ihre Lippe ist ein bisschen verletzt, aber sie lacht trotzdem.

It can mean either, depending on context.

At the start of a sentence, German always capitalizes the first word, so:

• ihre Lippe = her lip
• Ihre Lippe = your lip (formal)

But at the beginning of a sentence, both appear as Ihre.

So only the wider context tells you which one is meant. If the meaning shown to you is her lip, then this Ihre is the possessive her.

Because the possessive word has to take an ending that matches the noun.

Lippe is:

• feminine
• singular
• nominative here, because it is the subject of ist

So the possessive takes -e:

• ihre Lippe
• meine Hand
• deine Nase

This is why ihr Lippe would be incorrect.

Because the sentence is talking about one lip, not both lips.

German uses:

• die Lippe = lip
• die Lippen = lips

So:

• Ihre Lippe ist verletzt = Her lip is injured
• Ihre Lippen sind verletzt = Her lips are injured

Verletzt comes from the verb verletzen, meaning to injure or to hurt.

In this sentence, verletzt is being used after ist, so it functions like a predicate adjective:

• Ihre Lippe ist verletzt. = Her lip is injured.

Compare:

• Sie hat ihre Lippe verletzt. = She injured her lip.
• Ihre Lippe ist verletzt. = Her lip is injured.

So here the focus is on the state/result, not on the action itself.

Lowercase sie can mean:

• she
• they

Uppercase Sie means you in the formal sense.

Here it is lowercase, so it is not formal you.
And because the verb is lacht (singular), sie must mean she, not they.

So:

• sie lacht = she laughs
• sie lachen = they laugh

Because aber is a coordinating conjunction, and after it German usually keeps normal main-clause word order.

So you get:

• ..., aber sie lacht trotzdem.

This is normal:

• subject = sie
• verb = lacht

You would get lacht sie only if something else came first in the clause:

• ..., aber trotzdem lacht sie.

So both are possible, but they have slightly different emphasis.

Trotzdem is an adverb, and its position is fairly flexible.

In this sentence:

• ..., aber sie lacht trotzdem.

This sounds natural and means ..., but she laughs anyway / nevertheless.

You can also say:

• ..., aber trotzdem lacht sie.

Both are correct. The second version puts more emphasis on trotzdem.

So the final position here is not because it must be there, but because it fits the sentence naturally.

Ein bisschen means a little, a bit, or slightly.

So:

• ein bisschen verletzt = a little injured / slightly hurt

It softens the statement. It suggests the injury is not very serious.

Similar expressions are:

• ein wenig verletzt
• etwas verletzt

All of these are common, though ein bisschen is especially natural in everyday speech.

No. Lacht comes from lachen, which means to laugh.

So:

• sie lacht = she laughs / she is laughing

If you want she smiles, German usually uses:

• sie lächelt

So lacht trotzdem means she is still laughing, not just smiling.