Can we delete armor once in HoM?

Once we put the armor set into the Hall of Monuments, can we delete it from our inventory to make space?

Yes. Anything that goes in the HOM is there forever even if you delete it. Armor, weapons, minipets, whatever.

It's impossible to lose progress in the HoM. Once something is in, it's in for good, so yes, you can ditch whatever you like after dedicating it. You could delete all the characters on your account and it would still be fine. The only exception is if you get the account permanently banned, which would prevent it being linked to a GW2 account.

EDIT: Perhaps you has a poor choice of words, but rather than just deleting your armor it's worth salvaging it for some rare materials (won't be much but it's more than nothing) or selling it to the merchant.