Следовательница заподозрила, что свидетельница лжёт.

Because both nouns refer specifically to women.

• следовательница = a female investigator
• свидетельница = a female witness

In Russian, many nouns for people change form depending on gender. Here:

• masculine: следователь, свидетель
• feminine: следовательница, свидетельница

A useful nuance: свидетельница is a very normal feminine form. следовательница is understandable and used, but in real life Russian often still uses the masculine job title следователь even for a woman, depending on style and context. This sentence chooses the explicitly feminine form for both people.

In the past tense, Russian verbs agree with the subject in gender and number.

The subject of the main clause is следовательница, which is feminine singular, so the verb must also be feminine singular:

• masculine: заподозрил
• feminine: заподозрила
• neuter: заподозрило
• plural: заподозрили

So заподозрила tells you that the investigator is female.

что introduces a content clause, like English that.

So the structure is:

• Следовательница заподозрила = The investigator suspected
• что свидетельница лжёт = that the witness is lying

In other words, the whole clause что свидетельница лжёт is the thing being suspected.

Because in Russian, subordinate clauses are normally separated by a comma.

Here, что свидетельница лжёт is a subordinate clause attached to the main clause Следовательница заподозрила. So the comma is required:

• Следовательница заподозрила, что свидетельница лжёт.

This is much stricter than English, where that-clauses often have no comma.

Because each one is the subject of its own clause.

• In the main clause, следовательница is the subject of заподозрила.
• In the subordinate clause, свидетельница is the subject of лжёт.

So both stay in the nominative.

A helpful way to see it:

• Main clause: Следовательница заподозрила
• Subordinate clause: свидетельница лжёт

The object of заподозрила is not a noun here; it is the entire clause что свидетельница лжёт.

This is an aspect question.

• заподозрила is perfective
• подозревала is imperfective

заподозрила means she became suspicious or formed a suspicion at some point. It presents the suspicion as a completed event.

подозревала would mean she was suspecting or had suspicions over a period of time.

So:

• Следовательница заподозрила... = she came to suspect...
• Следовательница подозревала... = she suspected / had been suspecting...

Because Russian often uses the present tense in the subordinate clause when the action is understood as simultaneous with the main idea from that moment of suspicion.

So что свидетельница лжёт means the investigator suspected that the witness was lying / is lying.

Compare:

• что свидетельница лжёт = that the witness is lying
• что свидетельница лгала = that the witness was lying / had been lying
• что свидетельница солгала = that the witness lied once / told a lie

The version in your sentence focuses on the idea that the witness is giving false testimony, not just that she told one specific lie.

It is somewhat irregular from a learner’s point of view.

The infinitive is лгать. Its present-tense forms are:

• я лгу
• ты лжёшь
• он/она лжёт
• мы лжём
• вы лжёте
• они лгут

Notice the stem alternation:

• лг-
• лж-

That alternation is normal in Russian for some verbs, but you do need to memorize it.

Yes. In normal Russian writing, ё is often replaced by е, so you may see:

• лжёт
• лжет

They mean the same word. But for pronunciation and stress, ё matters:

• лжёт is pronounced with a yo sound, and the stress is on that syllable.

As a learner, it is useful to mentally restore ё when you can.

Yes, Russian word order is flexible, though the sentence as written is the most neutral and straightforward:

• Следовательница заподозрила, что свидетельница лжёт.

You can change the order for emphasis, but it becomes more marked or literary. For example:

• Что свидетельница лжёт, следовательница заподозрила не сразу.

That puts focus on the subordinate clause.

So the original order is the best default pattern for learners.

Yes. A very common alternative is:

• Следовательница заподозрила свидетельницу во лжи.

That means roughly The investigator suspected the witness of lying.

Comparison:

• заподозрила, что свидетельница лжёт = suspected that the witness is lying
• заподозрила свидетельницу во лжи = suspected the witness of lying

Both are natural. The version with что uses a full clause; the other uses a noun phrase во лжи.