Yes — Lightroom can create a bleach bypass look, and you do not need Nik plugins for it. You can even try Lightroom via a trial first, and standalone purchase was an option for Lightroom 6.

If you want a free way to experiment, GIMP is also a valid choice. It’s less powerful than Photoshop overall, but it’s perfectly capable for trying this effect, and there are tutorials available for creating a bleach bypass style in GIMP.

In Lightroom, you can make the effect yourself or use one of the many available presets. Presets can be a quick starting point, but they aren’t required.

So the short answer is:

• Lightroom: yes, workable for bleach bypass
• Nik plugins: not required
• GIMP: good free alternative for experimentation

If your main goal is simply to learn and test the look without subscribing, GIMP is the lowest-cost starting point; if you want a more polished photo workflow, Lightroom is a solid standalone option.