This is a configuration issue if I'm not mistaken namely your Lucene Index Configrations files within the App_Config/Includes folder. Most likely the Sitecore.ContentSearch.Lucene.DefaultIndexConfiguration.config file or a custom one created in your solution.
Usually you see these sorts of errors when a TypeConverter is missing from the config, as you can see its referencing the Typeconverter in the StackTrace. E.g. For the index to correctly convert DateTime this line is added to the DefaultIndexConfiguration.config file. Confirm the following line is in your *.DefaultIndexConfiguration.config file(s)
<converter handlesType="System.DateTime" typeConverter="Sitecore.ContentSearch.LuceneProvider.Converters.IndexFieldDateTimeValueConverter, Sitecore.ContentSearch.LuceneProvider" />
It's also worth identifying which Field is causing the error. Perhaps a new field has been added recently to a template or the raw value in a DateTime field is not in the correct format for a DateTime Sitecore stores its dates in ISO 8601 formatted i.e. yyyyMMddThhmmss