Yes, it indiscriminately affects both allies and enemies within its range.
If it was intended to only affect creatures that the Mummy Lord chose it would say so (many other abilities and spells have that distinction).
The Solar’s Searing Burst Legendary Action is an example of this, where it states:
Each creature of its choice in a 10-foot radius must ...
An important point to note is that being within 5 feet of the Mummy Lord is a very restrictive condition. It is unlikely to be fulfilled in a battle by its allies. The condition is much more likely to be fulfilled by its enemies.
Additionally, the Mummy Lord is a Legendary creature, and as such should be played by the DM with significant tactical acumen, so it will be aware of this consequence when choosing its Legendary Actions.
A follow up question from the comments deserves some additional attention:
Does the mummy have to make this saving throw itself?
A number of other monsters use this phrasing to signify the targeting of their actions/legendary actions:
- Demilich Howl (Action)
- Demilich Cloud of Dust (Legendary Action)
- Nalfeshnee Horror Nimbus (Action)
- Dragon Wing Attack (Legendary Action)
The clear intention of this phrasing is to target creatures other than the creature originating the effect.
If we were to take this phrasing to include the creature originating the effect, then we would have to conclude that the Dragon's Wing Attack can potentially deal bludgeoning damage to the Dragon itself and knock itself prone...after which it can fly up to half of it's flying speed.
D&D is written in natural language, as opposed to legal or technical language. As a result it needs to be interpreted. In that interpretation we should generally exclude the patently absurd (like a Dragon's Wing Attack having the ability to knock itself prone before it immediately flys away).
If we assume consistent application between the same natural language phrasing in different actions, then we have to conclude that the Mummy Lord is not targeting itself with this effect.
Additionally, the Legendary Action text states (emphasis mine):
Bliding dust and sand swirls magically around the mummy lord.
The fact that it is swirling around the Mummy Lord indicates that it is not swirling through the Mummy Lord's space.