Zoo re: lying and hwk etc.
lying is a sign of intelligence 
!
12 yrs is the classic age for this sort of stuff - avoidance of hwk - then lying to cover up. This too shall pass. Pay a lot of attention to one or two things that he excels in or that interest him. Avoid negative spiral. Keep telling him you have faith!
Dd went through a phase of lying and the best way of dealing with it (I found anyway after trying lots of different strategies) was to use humour ie not getting too heavy about it (which I found resulted in more covering up of things) but joking in such a way (ie gesturing of large pinocchio nose/exaggerating claims even further "oh don't tell me a large bat swooped down, stole your hwk, and flew out of the window") leaving culprit in no uncertain terms that you KNOW that they are lying. Other strategy with more serious things is to let them know you are disappointed because they are better than that etc etc and discussion (which I am sure you have already had) about lying to others is bad but lying to yourself is even worse!
taking away of phones/screens/games is good and getting him to "earn" phone time could be a good strategy ie 20 mins good quality homework = 10 mins of phone time!
make hwk a more collective activity with set times to set good habits? So snack and relax once home from school then 30 mins later all sit at table with telly off and do 20 or 30 mins - then break - then another 20 or 30 mins. You sit at the table too with your admin at the same time.
agree with Hills about rewarding effort not marks! Also agree if they don't see point they won't do it! Your ds is maybe a bit young yet, but in a couple of years, try and explore a few career ideas and see where he is at in terms of interests/what he wants to do job-wise. That can focus the mind
you may have heard me mention about a pedagogical talk I went to here in very high falutin' French (so missed lots of it!) but gist was that teens have huge brain plasticity and key years for absorbing and assimilating new facts etc is 14/15 yrs. It is around this age (in their view) that dc start to get the bit between their teeth and realise that it's up to them and no one else etc etc... so hang in there 
You have my sympathy though because, as you know, I nagged for England/Belgium when dd was a pre-teen about hwk, showering, putting stuff away, hanging stuff up, endless stuff ... . It is not perfect now but hugely improved so there is light at the end of the tunnel! 