The Crossway ESV German/English Parallel Bible (2018) seems to use the Luther 2017 German text "recently revised by a team of 70 experts and biblical scholars", not the original 1534 text. See this article to learn about the 2017 translation's goals and how the team (led by Christoph Kähler) tries to balance between original texts found since Luther's time AND Luther's classic formulation and sound (for liturgical use, such as the formality people expect and the Psalm's singability).
Archive.org has a scan of the 1535 edition, whose text maybe is close enough to the 1534 edition. In addition, I found 2 other versions that are a lot closer for digitizing purposes. The Logos version is fully digitized (and even has reverse interlinear) so by virtue of the software you can display it side by side with any English version.
A modern facsimile reproduction of the 1534 version, including the full-color artwork from the 117 original woodcut illustrations, can be purchased from the Biblical Heritage Exhibit Facsimile Bible Collections.
There is also a 1534 version published by German luxury art book publisher Taschen in 2003 edited by Stephan Füssel available here.
Archive.org (Google books scan)
Archive.org has a Google Books scan of the 1535 edition of the German Luther translation with a freely downloadable PDF (warning, very large file, 759 MB). But although the scan quality is very high and complete, it understandably uses the old German fonts that is rather hard to read.
It includes an 8 page introduction, deuterocanonical books, illustrations, 10 pages of what looks like a topical index, and 28 pages of chapter summaries.
CCEL (Christian Classics Ethereal Library) has an undated German Luther Translation available for online reading or for PDF download. Unfortunately, the only remarks is as follows:
This Bible translation was converted automatically from data files made available by the Unbound Bible project. Book names, introductions, titles, paragraphs, and the like were not available, so standard English names have been used. Therefore this file would benefit from additional work by someone who has access to a print edition.
I could not find the original from the now discontinued Biola University's Unbound Bible Project.
Logos Bible Software has created a digital version of the Luther Bible which they call Die Bibel nach Martin Luther (Luther 1984). It says:
The most important and influential of translations of the Bible into German is the Luther Bible. The influence that Martin Luther's translation had on the development of the German language is often compared to the influence the King James Version had on English. The Luther Bible is currently used in this revised version from 1984, which was adapted to the new German orthography in 1999. Despite the revisions, the language is still somewhat archaic and difficult for non-native speakers who want to learn the German language using a German translation of the Bible. This classic German translation of the Bible includes the apocrypha.
Logos.com said that it's the first German bible for which they have created a "reverse interlinear" feature", which can be purchased here.