Lad os rydde op i stuen, før vi går i seng.

Lad os means let’s.

It comes from the verb lade = to let.
Here, lad is the imperative form, so Lad os ... literally means Let us ...

So:

• Lad os gå = Let’s go
• Lad os spise = Let’s eat
• Lad os rydde op = Let’s tidy up

This is the normal Danish way to make a suggestion that includes the speaker.

Rydde op is a very common verb phrase meaning to tidy up.

• rydde on its own can mean clear, empty, or remove
• rydde op specifically means tidy up / clean up / put things in order

So op is not optional here if you want the meaning tidy up.

Compare:

• Vi rydder op = We’re tidying up
• Hun rydder bordet = She clears the table

Op is a particle, similar to how English uses up in tidy up, clean up, or pick up.

It helps create the full meaning of the expression rydde op.

In Danish, these particles are very common, and they often behave a bit like English phrasal verbs:

• stå op = get up
• tage af sted = set off / leave
• rydde op = tidy up

So it is best to learn rydde op as one unit of meaning.

I stuen means in the living room.

Here:

• i = in
• stuen = the living room

The basic noun is stue = living room, and the ending -n / -en works like the in English.

So:

• en stue = a living room
• stuen = the living room

Danish often uses i with rooms and enclosed spaces:

• i køkkenet = in the kitchen
• i soveværelset = in the bedroom
• i stuen = in the living room

Grammatically, i stuen is a location phrase, so it literally means tidy up in the living room.

But in real use, it often strongly implies that the living room is the area being tidied. So in natural English, it may very well be translated as Let’s tidy up the living room.

If you want to make the room more directly the thing being tidied, Danish can also say:

• Lad os rydde stuen op

That version makes stuen more clearly the object.
The sentence you were given is still very natural and common.

Før means before.

In this sentence, it introduces a subordinate clause:

• før vi går i seng = before we go to bed

So the structure is:

• main clause: Lad os rydde op i stuen
• subordinate clause: før vi går i seng

Also, før is used directly before a full clause. You do not add at after it here.

Correct:

• før vi går i seng

Not:

• før at vi går i seng

Because før vi går i seng is a subordinate clause.

The comma is acceptable and common in Danish. However, in modern Danish, the comma before a subordinate clause is often optional, depending on the comma style being used.

So both of these can be correct:

• Lad os rydde op i stuen, før vi går i seng.
• Lad os rydde op i stuen før vi går i seng.

The version with the comma can make the structure a little clearer for learners.

Because før introduces a subordinate clause, and subordinate clauses in Danish normally keep the subject before the verb.

So you get:

• før vi går i seng

not

• før går vi i seng

The verb-second pattern that Danish uses in main clauses does not apply in the same way here.

Compare:

• Main clause: Vi går i seng nu.
• Subordinate clause: ... før vi går i seng.

This is a very important word-order pattern in Danish.

Because Danish often uses the present tense to talk about future actions, especially when the time is already clear from the context.

Here, før already tells you that this will happen later:

• før vi går i seng = before we go to bed

So Danish does not need a special future form here.

This is very common:

• Vi ses i morgen = See you tomorrow
• Jeg kommer senere = I’ll come later
• før vi går i seng = before we go to bed

Gå i seng is a fixed expression meaning go to bed.

Literally, it looks like go in bed, but you should learn it as an idiom.

So:

• Vi går i seng = We go to bed / We’re going to bed

A useful comparison is:

• gå i seng = go to bed
• ligge i sengen = be lying in bed

Notice also the difference between:

• seng = bed
• sengen = the bed

In the expression gå i seng, Danish normally uses seng without the definite article.

Yes. A few natural alternatives are:

• Lad os rydde op i stuen før sengetid. = Let’s tidy up the living room before bedtime.
• Lad os rydde stuen op, før vi går i seng. = Let’s tidy the living room before we go to bed.
• Vi burde rydde op i stuen, før vi går i seng. = We should tidy up the living room before we go to bed.

Your original sentence is natural and idiomatic. It sounds like a friendly suggestion.