I don't like either of those sentences and doubt a native speaker would ever utter them. "Tomorrow I'll lie in the sun for two hours" would be my preference.
"I will have lain in the sun" suggests, to me, that the lying in the sun is continuous. This makes the use of "tomorrow" problematic since it is impossible to lie in the sun continuously from one day to another; eventually it gets dark. But you could say this: "By the end of the day I will have lain in the sun for 5 hours."