We live in the UK and my daughter has dual citizenship. However, she never entered the UK with her Brazilian passport, only with the German passport. Now we are travelling to Croatia without the German passport (lost). Will it be OK to reenter the UK with only her Brazilian passport?
You indicated in a comment that your wife has German citizenship, and that she will be traveling with your daughter (and with you, though that's not relevant for our purposes). Because of those facts, your daughter can benefit from freedom of movement as laid out in directive 2004/38/EC, as the family member of an EU citizen. It's therefore not necessary for her to prove German nationality as a condition of being granted indefinite entry. Instead, your wife can prove her German nationality and that your daughter is her child.
German embassies abroad can provide a "Reiseausweis als Passersatz" for Germans who have lost their papers. This is supposed to be used to get back to Germany, but according to German websites this is accepted by other EU countries as well.
I'd try to replace the German passport as quickly as possible.
It seems that as a Brazilian citizen, you can enter the UK without visa for six months. But you need a visa to join your family or partner in the UK for a long stay. Assuming that your daughter would want to stay with you long term in the UK, she'd need a visa.
Now since she is a German citizen, she doesn't need a visa, but the problem is that she might have to prove it at the border. If there is proof other than the passport that she has German citizenship, that might help (for example a German identity card, birth certificate etc.).
I'd really try to get a new passport, or at the very least contact some agency that would handle this - which may be hard to find, because it is such an unusual situation.
PS. If the customs officer asks how long she wants to stay in the UK, you have a problem. Because you would either be lying, which is bad, or you would stay that she wants to stay permanently, which is also bad.