Question: For example my hero currently does a `15%` lifesteal from it's basic attack of **50**.
When it trigger a critical strike doubling my damage to **100**, does my lifesteal also doubles the amount?

Is it the same for double damage?

Answer: 
Lifesteal is calculated after all damage enhancements and reductions have taken place.

So that means that any Skill, item, enhancement, aura or effect which increases your base damage will affect lifesteal, because it is applied AFTER all those have taken place. Except in cases where a `Conditional Modifier or Ability Modifier` takes priority (if lifesteal is from an item) [see wiki](http://www.dota2wiki.com/wiki/Unique_Attack_Modifier#Priority)

Examples

Critical Strike `Lifesteal is calculated after Critical Strikes` which means that it will increase the amount of life you steal.

Double Damage - `+100% damage on your base damage and any attribute increasing effects`
Also increases the amount of life you steal

[Dota 2 Wiki - Lifesteal](http://www.dota2wiki.com/wiki/LifeSteal)
Short answer is yes.

Practical answer; if you have lifesteal coming from a non orb source (aura, innate ex: lifestealer passive) it is almost always better mathematically to buy Desolator before critical strike against most targets with most armor values you are likely to see in game.