Are there any Web services available for your data?
There are several Web services that provide data of the most popular statistics. All information about Web services can be found here.
Is there a method to get data in such format that it would fit into an automated collection system?
For both the newest and historical data there are files in MS Excel format, updated on the release day. Each file has its own static link (for example, Balance Sheet of the Bank of Lithuania excel link), so with the appropriate software data can be updated by reading those files. The files contain both the newest and historical data, so on the release day all data revisions can be accessed as well.