Well, there’s the really simple answer of be an elan, which are immortal psionic creatures. Humans can theoretically become elans, though the process is deliberately left undescribed and up to the DM, plus it costs you all class levels, skills, feats, and so on (you start over as a 1st-level character).

Besides that, the psionic-magic item-creation transparency rules from Magic Item Compendium pg. 232 means that the regular lich template is probably available to humanoid psionic characters. The only requirement for becoming a lich is to be humanoid, and to be capable of crafting a phylactery, and a psionic character can craft psionic versions of magic items by doing the following:

• Substitute Craft Universal Item for Craft Wondrous Item.
• Substitute manifester level for caster level.
• Substitute “a psionic power of similar flavor” to craft an item that “includes a spell prerequisite, but the effect of the item does not directly implement the spell.” This seems like it should be more than sufficient to substitute “ability to manifest powers” for “ability to cast spells,” but it doesn’t come out and say that.

Interestingly, this is true even if playing with the “psionics is different” variant; Magic Item Compendium specifies that in that case, the item created this way is specifically psionic, but you can still do it.

Just for completeness’s sake, the extremely well-received third-party book Hyperconscious by Bruce Cordell (one of the primary authors of the Expanded Psionics Handbook) had a specific psionic lich adaptation.

But if you don’t buy that, don’t use that rule, or are not humanoid, there are other options.

The spectral savant from Complete Psionics is kind of mid-way between a lich or a vampire, and results in immortality. The grim psion even gets a kind of phylactery, though it is a 3.0 class that will require some adaptation. The psion uncarnate doesn’t actually say that you become immortal, but it’s kind of weird to imagine “a being of pure psionic consciousness” aging.

And then, just about any high-level psion can easily make a phylactery of sorts, though it does result in level-loss when you die, while a phylactery doesn’t.

An epic erudite takes the feat Epic Manifestation

Originally presented in the Epic Level Handbook under the Variant: Epic Psionic Seeds (102), the feat Epic Manifestation doesn't appear on the SRD's list of epic feats, instead appearing only in the text describing Epic Psionic Powers (making it a contender in the Most Obscure Feat competition), but the feat Epic Manifestation functions for a psion like the feat Epic Spellcasting functions for a caster.

The feat Epic Manifestation allows an epic erudite to convert 9th-level spells into powers because Epic Psionic Powers says

Generally, all the epic spell rules work for epic powers as well, except as noted below for displays.

and Epic Spell Levels says

Epic spells have no fixed level. However, for purposes of Concentration checks, spell resistance, and other possible situations where spell level is important, epic spells are all treated as if they were 10th-level spells.

Emphasis mine. An argument can be made that this is a case wherein spell level is important.

Note that, while this method is less shady than many alternatives (e.g. here, here, here), this method still needs the DM's approval, and I suspect some conservative DMs would tell the epic erudite to content himself with 9th-level psionic powers and 8th-level spells.