1) "If only he took as much exercise as I did he wouldn't have that spare lyre, I thought unsympathetically" (I looked it up in several dictionaries but I couldn't find anything, I know she implies her boyfriend is overweight but I don't understand how a musical instrument can be related to fat )
I think this is a typing mistake in the book - the correct phrase is "spare tyre" (American spelling is 'tire'), meaning the rubber part of a wheel. Sometimes, extra weight around the belly can look like the person is wearing a rubber tyre around their waist!
2) "It was an anonymous, almost commonplace face..." (I thought these two adjectives were synonyms, when they are used to talk about a person's facial features, am I correct?)
When used in this context, yes, they mean almost the same thing. An anonymous face is one that you can't identify. A commonplace face is one that you might see anywhere you go. The idea is that the person looks just like anyone else, and is maybe difficult to describe or remember.
3) "Now an orphan, I began to drift, often trying to stay one step ahead of the law- not so easy when you haven't always got somewhere to put your head down" (I guess the first phrase means trying not to get into trouble with the police and the other means having a place to sleep?)
You are mostly correct. 'Drifting' is moving around without a permanent home. "One step ahead of the law" means you are keeping out of the way of the police while doing possibly-illegal things. So not so much "trying not to get in trouble", but trying not to get caught!
4) "Roger managed to get his feet into the wrong slippers -always a fifty-fifty chance- before lumbering towards the bathroom" (does this mean that he gets his feet into the wrong slippers 50% of the time? I know the verb 'to lumber' means 'to walk slowly and awkwardly' but can it also be used for a drunk person or just a sleepy one like this case?)
You are correct with these!
5) "I could anticipate almost to the second when breakfast was ready" (could this phrase mean 'immediately'?)
This means that the person knows exactly when breakfast will be ready. Not necessarily immediately, but instead knowing the time in advance. For example, I can anticipate/predict the arrival of a Japanese train almost to the second, because they are so punctual and reliable. I always know when they are going to arrive.
From another story:
1) "His insolent voice was edged with menace" (Could this mean filled with menace?)
Imagine drawing a circle, and colouring it in blue. Then add some red to the outside of the circle, so that it has a red outline. The circle is blue, but is now edged with red. So basically it means that most of his voice sounds insolent, but there is a little bit of menace that is heard around the 'edges' - so just a hint of it.
2) 'to say evenly/unevenly' as in for instance: ''They are my things,'' he said evenly. or ''This is ridiculous'', he said unevenly. ''I must ask you...''
This means that the voice is either steady or unsteady. A calm, relaxed or confident person would speak evenly, without difficulty, but a nervous, upset or angry person might speak with pauses, hiccups, stammering or just having their voice wobble.
3) "She wanted Larry to learn to fight his own battles" (Could this mean that she wanted her son to defend himself? Her son is being bullied by another kid)
Yes, exactly! She wants her son to be confident, to learn to 'stick up for himself', and not rely on other people to defend him or help him out. (Whether or not this is a good idea in the bullying example is a controversial subject!)
I hope that helped!