Some Lutherans understand Paul to say that we are justified entirely through faith, but once he's done that, we're responsible for how we respond. That's how I understand this response from the LCMS:
https://www.lcms.org/about/beliefs/faqs/doctrine#lose.
Calvinists don't, but predestination complicates assessing the Calvinist position on loss of salvation.
For this reason I generally object to "salvation by faith alone." Paul taught "justification by faith alone." When he speaks of justification by faith it's clear he was excluding works.
Many NT scholars will say that we are justified by faith and judged according to works. When you take 1 Cor into account, Paul seems to say that. I believe Jesus does as well. The position I attribute to Lutherans, however, is not the only way to deal with this. While justified by faith and judged according to works is widely accepted, there are a number of understandings of how it works. This article attempts to show the major categories:
https://www.etsjets.org/files/JETS-PDFs/52/52-2/JETS 52-2 323-339 Ortlund.pdf
Another approach is to say that works inevitably follow from faith. I think that's a position I'd take. Jesus says that good trees produce good fruit. Note however that in the Reformed tradition, salvation includes all of the consequences of faith, so it includes both justification and the Christian life (works, sort of, but Paul aways uses works in a negative sense). This depends upon your concept of faith. I see Paul's faith as equivalent to Jesus' idea of being his follower. It's not precisely a set of actions, but it's an orientation that results in and is shown by actions. I don't think you can be a follower without following. That would be nonsense.