Deixis is when the meaning of a word is different depending on what the speaker is referring to; for example, if you use a pronoun (you, he, she, they), you do not explicitly state who you're referring to (you leave it to the speaker to work out exactly who you're talking about). An easy example of deixis would be the word "tomorrow"; it refers to the day after the current day, and thus without knowing what day it is currently, you can't deduce what the speaker means by "tomorrow".
Lexis is a little more difficult to simplify. From what I can deduce, it refers to the stock of words in a language that are most frequently used together (as it means we don't have to think through every sentence we construct word-by-word before saying it, and can instead connect short phrases together to create meaning). Essentially it's a tool which allows us to take a linguistic short-cut and avoid having to construct sentences from scratch, thus worrying about grammar and such. We select appropriate combinations of words from our lexis to fit the register (context) of the situation (words can often mean different things when referring to different topics) and to fit the generally socially accepted patterns of speech that people follow when discussing topics.