Learn Portuguese (Portugal): Têm-se de proteger as lombadas dos livros. - The spines of the books have to be protected.

Because this sentence uses the passive se. In this structure, the things being protected (as lombadas) act as the grammatical subject of the sentence, not just the object. Since as lombadas is plural, the conjugated modal verb must also be plural (têm) to agree with it.

Why does the -se attach to têm rather than the main verb proteger?

In European Portuguese, when using a modal verb phrase like ter de followed by an infinitive, the pronoun typically attaches to the conjugated auxiliary verb (têm-se de proteger). While you might sometimes hear it attached to the infinitive in casual speech, putting it on the conjugated verb is the standard rule for neutral, affirmative sentences.

Could I say Têm-se que proteger instead of Têm-se de proteger?

In strict European Portuguese grammar, ter de is the correct form for expressing obligation (having to do something). You will hear ter que very often in casual speech, but traditionally it is meant for situations where you physically have items to deal with, rather than a general rule or moral obligation. It is best to stick to ter de here.

Does the word lombada only refer to the spine of a book?