DCA is effective in the process of averaging against volatility and putting purchases in an ordinary income stream, however, when you have a lump sum, it may be worthwhile to buy on the downside or buy more actively. It all depends on whether you have an effective plan and with a clear plan, you should not touch on monies that are likely to impact on your necessities. Basically, both strategies can be applied using the same capital, it is primarily a matter of timing, risk-taking, and disciplineness when using discretionary funds.
The discretionary income to be used depends on the level of your comfort and not even about the market environment and If you say buying on a Lump sum is worth while buying on the down side then to me you are describing buying the dip and not buying with the lump sum, because talking about buying with the lump sum has nothing to do with the market conditions but rather an investor decision to buy immediately with the available Lump sum amount irrespective of the market conditions,
You are right, however I believe that some people prefer not to invest all of their money at once without thinking about market conditions first. Sure, a lump sum means you invest everything all at once, but not everyone is comfortable with that. Many people choose to wait for a better price before investing their money, because no one wants to buy when the market is too high.
So, buying the dip and lump sum are not the same thing, it's just that people do their things differently. Some may decide to invest their money once, while others will wait for a dip. But, in the end, it will depends on how the person thinks and the kind of risk they are willing to take.
It seems the point of this discussion is veering towards buying bitcoin when the price is low. Because what's meant by buying at a better price is clearly meant to mean buying at a lower or falling price. I don't mind that, as we're all free to invest our money in bitcoin in any way. But I think such things are better done by individuals without having to advise others. This can certainly undermine someone's intention to invest in bitcoin. Someone who initially intended to do DCA could change their mind after seeing your assumptions.
Furthermore, waiting for the bitcoin price to drop before making a purchase will also cause us to lose momentum. Especially if we wait for the bitcoin price to drop to, say, $30,000 or even lower. I believe if someone waits for the bitcoin price to drop that far before making a purchase, I think they will ultimately not invest in bitcoin. This is because they're waiting too long, and what they're waiting for will never come. Therefore, if you're going to invest in bitcoin, buy immediately, provided you have discretionary funds.