What do you mean? Private companies can certainly make strategic investments in other private companies to commoditize complements, partner on technology, explore potential M&A and for other reasons too.
I can understand a strategic acquisition, but this is just a long-term investment. I can see how the two companies relate (Stripe loves to be there at the inception of engineering ideas), but I just imagine investing in something that won't return your capital for years to come while you're still strapped for cash being a little... odd?
I agree that they don't seem like they're strapped for cash, but it's still a strange use of investors' capital. If Stripe's investors wanted to invest in Lambda School, why wouldn't they just do so directly? And since Stripe evidently didn't need the full $250M for its own operations and initiatives, why didn't it just raise less?
I think there are ways to spin Stripe's investment as a customer acquisition play. If they have more influence over Lambda School curriculum or partnerships by merit of being an investor, and Lambda School is churning out web developers whose first instinct is to turn to Stripe for all things billing, that seems like a pretty reasonable use of investor capital to me.
Someone made a similar comment about YC a few weeks ago – how if you were building dev tools, even though $150k for 7% results in a lower valuation than many founders could find elsewhere, you could consider the equity the price for access to the YC network and existing companies to use your product.
See: Coinbase Ventures, Slack's fund, etc.