How to handle non consistent time series( using LSTM )
If you have missing data you can add a Masking layer to your model which will prevent contributions from those time steps to be included.  You can see the documentation for it here: https://keras.io/layers/core/#masking

Example taken from the keras documentation: 


  Consider a Numpy data array x of shape (samples, timesteps, features),
  to be fed to an LSTM layer. You want to mask timestep #3 and #5
  because you lack data for these timesteps. You can:
  
  set x[:, 3, :] = 0. and x[:, 5, :] = 0. insert a Masking layer with
  mask_value=0. before the LSTM layer:


With example code:

model = Sequential()
model.add(Masking(mask_value=0., input_shape=(timesteps, features)))
model.add(LSTM(32))