First, you have PALATALIZED "Л" here. This means that you pronounce L with your tongue high in your mouth. In "Лама" you pronounce "L" with your tongue low and brough back a bit. Second, you have some good ears! It is indeed [dl'i]. In Russian unstressed "И", "Е"(Э) and "Я" sound the same. It is an unclear sound between И and Э. The sound is close to how native English speakers pronounce "i" in "hit".

We (russians) pronounce it as 'dlya minya'. Put the accent on the last syllable. Для менЯ

You can listen how to pronounce it here http://www.forvo.com/word/%D0%B4%D0%BB%D1%8F_%D0%BC%D0%B5%D0%BD%D1%8F/#ru