Después de lavar la lechuga, la dejo en el escurridor mientras mi hermana busca el batidor.

Because after después de, Spanish normally uses an infinitive when it means after doing something.

So:

• después de lavar la lechuga = after washing the lettuce

You would not say después de lavo.

A useful pattern is:

• después de + infinitive

Examples:

• después de comer = after eating
• después de estudiar = after studying
• después de lavar la lechuga = after washing the lettuce

If you want to name a different subject, Spanish often uses después de que + verb instead:

• Después de que mi hermana lave la lechuga...
• Después de que mi hermana lavó la lechuga...

But in your sentence, the infinitive structure is the natural one.

La is a direct object pronoun, and here it means it.

It refers back to la lechuga.

So:

• la lechuga = the lettuce
• la dejo = I leave it

Spanish uses object pronouns a lot to avoid repeating the noun. In English, we do the same:

• I wash the lettuce, then I leave it in the drainer.

Because lechuga is feminine singular, the pronoun is la.

This is completely normal in Spanish. The first mention introduces the noun:

• lavar la lechuga

Then the second clause refers back to it with a pronoun:

• la dejo en el escurridor

English does the same:

• After washing the lettuce, I leave it in the drainer.

Without la, the sentence would feel incomplete, because dejar here needs an object: you are leaving something somewhere.

Because Spanish often omits subject pronouns when they are already clear from the verb ending.

• dejo already means I leave
• busca already means he/she looks for

So:

• la dejo = I leave it
• mi hermana busca = my sister looks for / is looking for

Adding yo is possible, but usually unnecessary unless you want emphasis or contrast:

• Yo la dejo, pero ella no. = I leave it, but she doesn’t.

Spanish uses definite articles (el, la, los, las) more often than English.

Here they sound natural because the speaker is referring to specific things in the kitchen context:

• la lechuga = the lettuce being prepared
• el escurridor = the drainer/colander being used
• el batidor = the whisk/beater being looked for

English sometimes drops the where Spanish keeps it, especially with food or general household items. So this is a good area to get used to Spanish sounding a bit more article-heavy than English.

Here dejo means something like I leave it or I put it and leave it there.

The verb dejar is very common and can mean:

• to leave
• to let
• to put something somewhere and leave it there

In this sentence:

• la dejo en el escurridor

the idea is not I abandon it, but rather:

• I leave it in the drainer
• I put it in the drainer and let it stay there

That is a very natural use of dejar.

Because en is the normal preposition for location here: in/on the drainer.

So:

• dejar algo en algún sitio = to leave something somewhere

Examples:

• Dejo las llaves en la mesa. = I leave the keys on the table.
• Dejo la sopa en la cocina. = I leave the soup in the kitchen.
• Dejo la lechuga en el escurridor. = I leave the lettuce in the drainer.

Using a here would not sound right.

Escurridor is something used for draining water off food or dishes.

Depending on context, it can mean things like:

• a drainer
• a colander
• a drying rack
• sometimes a salad spinner/draining container, depending on the exact object

In this sentence, because it is about lettuce, the most natural idea is a container or tool used to let the lettuce drain after washing.

So the key idea is: something where water drains off.

No, they are not the same.

• batidor usually means a whisk or beater
• batidora usually means an electric mixer/blender-type appliance

So in this sentence:

• mi hermana busca el batidor

the sister is looking for a whisk/beater, not a large appliance.

In Spain, people may also say varillas for a whisk, depending on the exact utensil and region, but batidor is understandable and correct.

Because Spanish often uses the present tense to describe:

• a routine
• a habitual action
• a step in a process
• a vivid scene

So the sentence can sound like:

• this is what I usually do
• this is what happens in this situation
• I’m describing the action as if it’s happening now

Also, mientras means while, so the two actions are presented as happening at the same time:

• I leave the lettuce in the drainer
• while my sister looks for the whisk

English can also do this:

• I leave it there while my sister looks for the whisk.

Yes, absolutely.

You could say:

• Después de lavarla, la dejo en el escurridor...

Here, lavarla means to wash it, with la attached to the infinitive.

Both versions are correct:

• Después de lavar la lechuga...
• Después de lavarla...

The full noun version is a bit more explicit, while the pronoun version is more compact. Spanish allows both.

Mientras means while and introduces an action happening at the same time as the main action.

So:

• la dejo en el escurridor = I leave it in the drainer
• mientras mi hermana busca el batidor = while my sister looks for the whisk

It links the two parts and shows simultaneity.

A simple pattern is:

• acción 1 + mientras + acción 2

Example:

• Yo cocino mientras él pone la mesa. = I cook while he sets the table.

So in your sentence, mientras tells you both kitchen actions overlap in time.