You have to ask your GM

The effect of custom wishes is entirely in the purview of the GM. We get this quote from the spell description:

This spell might simply fail, the effect you desire might only be partly achieved, or you might suffer some unforeseen consequence as a result of how you worded the wish.

Any of these possibilities and so many more could be an option in this circumstance.

Some things for the GM to consider

• The wording of the wishes. Wish has traditionally been a spell heavily influenced by wording so perhaps wishing the item to appear at your side teleports the lich with the item since the lich is not the rightful owner (perhaps the artifact was stolen). I'd be careful when abusing wording as the player can sometimes feel cheated or duped.
• Unforeseen consequences. This is usually my favorite approach for "game-breaking" wishes. If the lich having the artifact is integral to the plot, perhaps the item divides into two parts. I've used this method before and it leads to lots of interesting developments, especially if the artifact gains the desire to be united adjusting its usefulness for both the PC and the NPC.
• It might just fail. While this is often dissatisfying for the player, when properly described it can lead to a deal of gravitas with the situation. I've said things like "a great reality-fixing magic holds the artifact to the lich and your words of power are unable to separate the entities. The wish fails." (with different context of course). This shows the players the vast power of the lich and encourages more precaution when preparing to combat the creature.
• What's more fun? What it mostly boils down to is what is best for the game so that everyone has a good time. This will depend on the table and the players involved (including the GM). Wish is a very fun spell when used properly and can lead to many shenanigans that spice up the story. Treating custom wishes like a plot steer-er rather than a set-in-stone mechanical option is the best approach from my experience.

Option 2: both the caster and the steed will benefit, provided you Wish from something that only targets yourself.

Wish can create many different effects, but choosing which effect you want is part of the casting of the spell, so the steed won't be able to choose for itself the effect it wants. Whatever effect the caster creates will also apply to the steed.

However, the effect needs to be one that "targets only you". Here are the possibilities:

• Duplicate the effects of any other spell 8th level or lower: affects the steed if the spell you are duplicating only affects you (depends on the spell).
• Create one object worth 25000gp: doesn't target you, so it doesn't target the steed.
• Restore all hitpoints to up to 20 creatures: If you only choose yourself, then it targets the steed as well, but you could just choose yourself AND the steed AND others.
• Grant resistance to a damage type to up to 10 creatures: same as above.
• Grant immunity to a specific effect for 8 hours to up to 10 creatures: same as above.
• Undo a single recent event: doesn't target you, so it doesn't target the steed.
• Other (any creative use of the spell): if it only targets/affects you, then it will affect the steed as well (But you could also word it so that it affects the 2 of your regardless).

As we can see, there aren't a lot of actual benefits to sharing Wish with your steed, but you could do some fun things by duplicating spells.