Switching default male pronoun to default female, in deference to Wizards’ own style and to match rules quotes.
Her wizard class features give her no special ability to activate the item
As she does not have access to Enchantment or Evocation spells, she does not qualify as having those spells on her spell list for the purposes of activating spell-completion and spell-trigger items (e.g. scrolls and wands), even for spells that are otherwise on the wizard spell list. The School Specialization sidebar makes that much, at least, quite clear:
Spells of the prohibited school or schools are not available to the wizard, and she can’t even cast such spells from scrolls or fire them from wands. (PHB1 p57)
However, Use Magic Device is all about using items you usually can’t
A wizard could use the Use Magic Device skill to activate such items, the same as any other character. Wizards don’t get Use Magic Device in-class and don’t tend to invest heavily in Charisma, but the loremaster prestige class is really easy for a wizard to enter, and would get you Use Magic Device.
Anyway, that a wizard can Use Magic Device on spell-completion and spell-trigger items is, unfortunately, not immediately clear from the rule I quoted: that rule says they are not available, with no qualifications. Unfortunately, Wizards had this tendency, particularly early on, to assume single-classed characters, and ignored cross-class skills. It probably simplified the language, but at the cost of making things confusing when you stepped away from those assumptions.
For this, I am going to draw parallels to the question of whether or not a multiclass specialist wizard may cast spells of her banned school with her other class. The books explicitly allow this (Complete Arcane 185), despite that very same rule I’ve quoted above which seems to say that the specialist wizard may not cast those spells at all. What that line actually means is that the wizard class itself does not give you the ability to cast those spells or use those items when you specialize and ban those schools. You can still use the usual methods around that inability, the same as, say, a monk could.
You can apply class abilities to spell casting from magical items
While casting from an item is not the same as a Casting a Spell action, it is still casting a spell. Unless a term is given a special definition in 5e game terms, you use the common definition for that term. You are casting the spell, the ability to do so comes from the item. For instance, the Staff of Fireballs:
.. you can use an action to ... cast one of the following Spells ...
Is no different, in this regard, to Wand of Fireballs from:
you can use an action to ... cast the Fireball spell ...
Jeremy Crawford has posted a number of answers we can point to in the time since this question appeared that verifies this really is the case. Each time he's been asked about a specific class ability the answer has been an affirmative. These were made when his tweets were official rulings, but since have been "downgraded" by the Sage Advice Compendium to his personal advice and perspective. While this is true, it still is clarification of the intent of the designers.
Metamagic
Can Metamagic be used on magic item casting a spell? Yes.
If a magic item's description says you cast a spell from it, you can use Metamagic on the spell. #DnD
and
Metamagic works w/ any spells that sorcerers cast. Wild Magic Surge can work w/ any sorcerer spell they cast. #DnD
Wild Magic
Can using a magic item cause a Wild Magic Surge? Yes
Yes.
Arcane Ward
Can casting from a wand/staff recharge Arcane Ward? Yes
Arcane Ward/Twinned Spell works when you cast a qualifying spell. It even works when an item says you cast one. #DnD
Best Answer
The Lore Master's abilities don't work with spells cast from items
Unfortunately, the Lore Master's Spell Secrets and Alchemical Casting features both have a more restrictive wording than the Sorcerer's metamagic, as they specify the restriction (emphasis mine):
If you didn't use a spell slot to cast the spell, it's not eligible to be affected by these features. As a general rule, spells cast from items do so without using your own slots (emphasis mine):
If you had a magic item which explicitly let you cast a certain spell using your own spell slots, then a spell cast in that way should qualify for these effects; but I can't think of any such items off the top of my head, and they would be the exception rather than the rule.