Inquist has already identified in his answer the sense of 'responsibility' used in the text. Thus, here I will focus only on the second part of your question:
It is telling about what the prosecutor made of the athlete. The athlete was self-centred, scornful of lacking responsibility in who? In his girlfriend? In himself?
'Responsibility' can take prepositions 'for' and 'to', but not preposition 'in'. In fact, the meaning changes completely:
A. Oscar Pistorius has a responsibility for his girlfriend
means he has a duty to care for his girlfriend
B. Oscar Pistorius has a responsibility to this girlfriend
means he has to account for his actions to his girlfriend.
I guess you meant the sense in A. I agree with Inquist that this is not the sense of "lacking responsibility" used in the BBC text. In fact, the prosecutor has accused Oscar Pistorius of avoiding responsibility not only for shooting at his girlfriend but also for shooting at a number of other public spaces (a restaurant, a boat party, a moving car...).
Prepositions taken by noun 'responsibility'
'Responsibility' does not take the preposition 'in'. If you want to know what prepositions a word takes, you can look up a collocations dictionary (for example: ozdic.com).
In this dictionary you will find that 'responsibility' can take prepositions 'for' and 'to':
responsibility for + (job/duty)
They're responsible for cleaning the engine
responsibility for + (failure/mistake/crime)
Who was responsible for the mistake?
responsibility for + (consequence)
To what degree do I accept responsibility for the success of each of my students?
responsibility to + (somebody/something)
The prime minister is directly responsible to Parliament.
Note that although 'ozdic.com' does not include the preposition 'toward', it is possible to use it with the same meaning as 'to':
'Responsibility' can also take the preposition 'of':