Coordinémonos, no vaya a ser que investiguemos lo mismo.

Coordinémonos is the affirmative nosotros command of coordinarse: let’s coordinate / let’s coordinate with each other.

• coordinamos = we coordinate or we coordinated, depending on context
• coordinemos = the nosotros subjunctive, which is also the base form used for the nosotros command
• coordinémonos = coordinemos + nos

The nos is attached to the end because affirmative commands in Spanish attach object/reflexive pronouns.

Here it is reflexive/reciprocal, so it means something like let’s get coordinated with each other or simply let’s coordinate.

When you attach -nos to an affirmative command, Spanish often adds a written accent to keep the original stress.

Without the pronoun:

• coordinemos

With the pronoun:

• coordinémonos

The accent on é shows that the stress still falls where it should. This is a very common pattern with affirmative commands plus attached pronouns.

No vaya a ser que is a very common idiomatic expression meaning something like:

• lest
• in case
• just in case
• so that it doesn’t happen that
• for fear that

In natural English here, it would sound like:

• Let’s coordinate, so we don’t end up investigating the same thing.
• Let’s coordinate, in case we investigate the same thing.
• Let’s coordinate, so we don’t both investigate the same thing.

It introduces a possible undesirable situation that the speaker wants to avoid.

Vaya is the present subjunctive form of ir for él/ella/usted.

In the fixed expression no vaya a ser que, Spanish uses this subjunctive form idiomatically. You do not need to interpret it literally as a normal use of ir. The whole phrase functions as a set expression meaning lest / in case / so that it doesn’t happen that.

So it is best learned as a chunk:

• no vaya a ser que + subjunctive

Because no vaya a ser que is followed by the subjunctive.

The speaker is talking about a possible or feared situation, not a straightforward fact. That is exactly the kind of context that triggers the subjunctive in Spanish.

So:

• no vaya a ser que investiguemos lo mismo

means:

• so that we don’t end up investigating the same thing
• lest we investigate the same thing

Using the indicative here would sound wrong.

Because this is not a statement of fact like we investigate or we investigated. It is a hypothetical possibility after no vaya a ser que, so Spanish requires the subjunctive:

• investigamos = indicative
• investiguemos = present subjunctive

Also note the spelling:

• infinitive: investigar
• subjunctive: investigue, investigues, investiguemos...

The g → gu change keeps the hard g sound before e.

Lo mismo means the same thing.

In this sentence:

• investiguemos lo mismo = we investigate the same thing

Spanish often uses lo + adjective to refer to an abstract idea or unspecified thing:

• lo importante = the important thing
• lo raro = the strange thing
• lo mismo = the same thing

So lo mismo is completely natural here.

In Spanish, investigar can cover both ideas depending on context.

It can mean:

• to investigate
• to research

So investiguemos lo mismo could mean:

• we investigate the same thing
• we research the same topic

In an academic or professional context, many English speakers would probably understand this sentence more naturally as research the same thing.

It is correct and natural, but in everyday speech people might also say things like:

• Vamos a coordinarnos
• Hay que coordinarnos
• Mejor nos coordinamos

All of these can express a similar idea.

Coordinémonos sounds a bit more direct and purposeful because it is a command: let’s coordinate.

It is not overly formal, but it is a little more compact and deliberate than some alternatives.

It is mostly neutral in register.

The form coordinémonos is a nosotros command, so it does not correspond to English-style formal vs informal you. It includes the speaker: let’s...

The expression no vaya a ser que is very common and natural. It can sound slightly careful, cautious, or strategic, but not especially formal.

So overall the sentence feels like normal educated Spanish that could be used in work, study, or everyday coordination.

Not very well. A very literal translation would sound awkward in English. It is much better to translate the idea rather than the words.

Good natural translations include:

• Let’s coordinate, so we don’t investigate the same thing.
• Let’s coordinate, in case we end up investigating the same thing.
• Let’s coordinate, so that we don’t both research the same thing.

So although the literal pieces are interesting grammatically, the whole expression should really be learned as an idiom.