Alzheimer's Disease (AD) is nowadays the most common form of dementia, and its automatic detection can help to identify symptoms at early stages, so that preventive actions can be carried out. Moreover, non-intrusive techniques based on spoken data are crucial for the development of AD automatic detection systems. In this light, this paper is presented as a contribution to the ADReSS Challenge, aiming at improving AD automatic detection from spontaneous speech. To this end, recordings from 108 participants, which are age-, gender-, and AD condition-balanced, have been used as training set to perform two different tasks: classification into AD/non-AD conditions, and regression over the Mini-Mental State Examination (MMSE) scores. Both tasks have been performed extracting 28 features from speech -- based on prosody and voice quality -- and 51 features from the transcriptions -- based on lexical and turn-taking information. Our results achieved up to 87.5 % of classification accuracy using a Random Forest classifier, and 4.54 of RMSE using a linear regression with stochastic gradient descent over the provided test set. This shows promising results in the automatic detection of Alzheimer's Disease through speech and lexical features.