This is a good question and it depends on the job. The fact that you say 'lying' implies that it wasn't remotely a SWE job, BUUUUUT, dev ops roles can vary. Some companies have dev ops under engineering, some have it under IT, some have it as it's own department.
If you were a "dev ops engineer" on a team under the "Engineering" organization and your work involved a lot of software in the same codebases as a "typical SWE", then you can probably get away with putting "Software Engineer" on your resume.
If you were fairly isolated, never wrote code and just configured AWS/Google Cloud/Azure all day, then I probably wouldn't say "Software Engineer" on your resume because it misrepresents what you actually did.
It's generally ok if background checks have different job titles. When you fill out the info for the background check, you should use the official title, so their verification process will match. The purpose of a background check is to make sure the info you submit on the background check is correct.
u/connic1983 wrote (the comment Michael replied to):
What about background checks that don’t request you to add your work history?
u/michaelnovatireplied·
Every background check asks for it, but you have to supply it for the background check specifically and it's not pulled from your resume directly. So when you provide it for the background check - use the official/on-paper job title
u/Daily_Internet_User wrote (the comment Michael replied to):
Will the recruiter ever ask or be suspicious that the title you put for the background check doesn't match the one on your resume?
u/michaelnovatireplied·
It depends on the company, but the background check company will typically produce a report. The report is checking that what you submitted to them matches what they can confirm with sources. Sometimes the source (i.e. your school or old company) won't reply and it will come back "unconfirmed". That doesn't mean you fail the check, but it will get flagged. Then someone in HR will review the report.
For most companies they are looking for red flags and major inaccuracies or falsehoods or a criminal record w/felonies.
If it was flagged then you would have to just explain, and if you aren't lying, but rather just using a different label for the job, then you'll likely be fine. If you were misleading them then they might rescind the offer.
So as with most things in life, "it depends"