No, you shouldn't just get more LP after a winstreak.
Say you have a certain MMR (Matchmaking Rating). After the winstreak, you play versus better opponents. But your MMR is lower than theirs. Therefore, you have to 'proof' your skill to the system and continue to win. After a winstreak, your MMR can be a little higher. You'll play against slightly better opponents, but not the ones you've ended your winstreak with. This will make sure your LP winnings (and thus your ranking) is according to your MMR.
You may not have won more LP, but you've definately gained some MMR. This means that if you end up against the exact same opponents you've started your winstreak with, you'll gain more LP after winning from them, because your MMR would say you are better than them and thus deserve to gain more LP.
You've also stated you are Bronze I. That is an exceptional class (all I's), where you have to prove you are really ready to move up a division (which is, in terms of regular play, 'permanent'). You cannot downgrade to Bronze (unless you don't play for a long time) so you have to prove you are up for silver (and thus raise your MMR accordingly).
TL:DR: The harder your enemies get, if you defeat them, the less LP you get but the more your MMR rises. The harder your enemies get, if you lose against them, the less LP you lose and the less your MMR goes down.
The easier your enemies get, if you defeat them, the more LP you get and the less MMR you rise (so you will be even 'better' then your enemies). The easier your enemies get, if you lose against them, the more LP you lose and the more your MMR goes down.
The point where the definition of your enemy goes from 'he is easier' to 'he is harder' is your current MMR.