Why LSTM models do not require labels for each step?
Time-series analysis has two main goals: 


To identifying the nature of the phenomenon represented by the sequence of observations, and 
To forecast (predicting future values in time for a variable).


NOTE: In this respect, models try to get pattern using historical values. Do not confuse here between forecasting (predicting future values) and prediction. 

For time-series prediction(forecasting) problems, the models ( ARIMA, LSTM) try to extract trend, seasonality, and residual from the list of historical values e.g. price from 300 historical dates or time. Therefore, there is no need to look for dependent variables here.
We must be clear, the time series forecasting algorithm extrapolate historical trend to near and far future. They do not predict target variable based on dependent variables. This is the main reason you will see time-series models only work with single variable who's historical data-points become input and future data points become target. 

Reference:


http://www.statsoft.com/Textbook/Time-Series-Analysis