You are very sweet and very brave for watching your friends children for a week. More than likely it sounds like its going to be a long week but the good news is that it is only one week. My advice to you about the lies is to not give him a chance to lie. For example, if he/she sneaks downstairs late at night for a snack and then tries to cover it up. Normally you might ask him "did you do this?", instead tell him "I noticed you came downstairs last night for a snack, were you hungry? It is ok if you were but next time lets ask and see if we can get you something that sounds good to eat." I have found that most often open ended questions(the ones with yes or no answers) most always end in denial. Let him know that you have noticed what he may have done wrong and how to fix it.
Its ok that you are more strict that the others. but maybe keep in mind that you dont have to parent these children. Instead look at it more like entertaining guests. While their parents are on holiday, these children also are on holiday from their parents. Let them know that there are rules in your home and while the rules are being followed lets have some fun. Keep them occupied and busy and keep it fun. It will be less stressful for them and for you and time will go by more quickly. And remember its only one week.
Hope this may help a little.