なくしては / なくして

なくしては means "without": it follows a noun, and the clause after it says what cannot happen without that thing. It belongs to formal writing and speeches.

The clause after なくしては is negative: ない, できない, あり得ない, 不可能だ, or "would not have" in the past. It can also be a question that expects "no". The noun is something the speaker treats as indispensable, and a comma usually follows は.

For a plain "without" that describes how something is done, use なしで.

• × 砂糖なくしてコーヒーを飲む → 砂糖なしでコーヒーを飲む

なくしては or なくして

Without は, なくして means the same and is just as formal. は puts a little more weight on the condition.

Register

なくしては is written Japanese. なしでは and なしには say the same in a lower register, and in conversation you say がなければ.

Not the verb なくす

なくして looks like the て-form of なくす, "to lose", but here it is なく, from ない, plus the written connective して. The noun takes no particle. With を in front, the same sound is the verb, and the sentence means something else.