I assume by “Alpinism” that you actually mean some form of mtneering involving mixed snow/ice and rock routes and not simply being out in the snow in Winter on a backpack.
The Lunar Solo is not suited for Winter use. No snowload capabilities and I think you will just be asking for it under the conditions you describe. I know the weight and price are tempting but… The Golite Hex or BD ‘mids would be far better suited but only if you learn proper set-up for extreme conditions. These involve digging in a snow platform, building a snowblock or snow wall and learning proper anchoring techniques w/ a variety of different anchors (bollards, pickets, flukes, skis, snow-filled stuffsacks, etc.). These are great for a basecamp but less suited to take along on an alpine route.
Far easier for many would be a “freestanding” dome -style tent such as the Biblers or ID’s . I, personally like the BD Epic canopied tents for Alpine Winter use. They are extremely light, strong for their weight, and I have been well served by them. There’s an amazing picture of a BD Firstlight perched on a precarious platform on Nanga Parbat in the latest Patagonia catalogue. These style tents require a smaller tent platform—-important if you are planning to set up shelter in problematic sites like ridge tops and ledges. These are true alpine-style tents.
I also use the BD ‘mids on ski touring trips which have performed well in some pretty bang up blizzards. These are fairly popular for Sierra ski trips. People have skied the JMT using these as their sole shelter.
Among tunnel style tents, I would suggest one of the Stephenson Warmlite tents w/ 3rd pole option to enhance wind and snow stability.