ADA applicability is usually more a matter of the magnitude of the effect than whatever the specific cause is.
Under the ADA, an individual with a disability is a person who:
- has a physical or mental impairment that substantially limits one or more major life activities;
- has a record of such an impairment; or
- is regarded as having such an impairment.
Example:
A person who cannot read due to dyslexia is an individual with a disability because dyslexia, which is a learning disability, is an impairment. But a person who cannot read because she dropped out of school is not an individual with a disability, because lack of education is not an impairment.
But the inability to read (and presumably write) only constitutes a disability if a) it substantially limits one or more major life activities, b) she has a record of having an impairment that substantially limits one or more major life activities, or c) it is believed that her dyslexia is such that it substantially limits one or more major life activities.
This is more difficult since Toyota. In Toyota, the Supremes ruled that inability to do a specific job does not mean that the impairment "substantially limits one or more major life activities".
"Justice O’Connor delivered the Court’s unanimous opinion reversing the appeals court, holding that the Sixth Circuit erred by analyzing only a limited class of manual tasks associated with Ms. Williams’ job. The appeals court should have asked whether Williams’ impairments restricted her from performing manual tasks that are of central importance to most people’s daily lives. The Court found that occupation-specific manual tasks may have only limited relevance if they are not an important part of most people’s daily lives. In this case, the Sixth Circuit should not have disregarded Williams’ ability to do other manual tasks of central importance, such as household chores, bathing, and brushing her teeth."
I would assume that the same would hold true, mutatis mutandis, for a mental disability. Whether or not reading and writing are considered central to most people's daily lives according to the courts, I do not know. If I had to guess, I'd say she was covered, meaning she's entitled to ask for you to enter into an "interactive process" in which you hope to arrive at a reasonable accomodation. The question then becomes, what is an appropriate accomodation? That depends a lot on what her job is. In the end, she has to be able to perform her job according to reasonable standards with or withotu accomodation.
She's told you that she has dyslexia. Has she told you that in the context of explaining her work performance problem? When you told her to carry around a dictionary, that sounds to me like it could be taken as the beginning of an interactive process or (less likely) even an accomodation. If you want to avoid going through the ADA accomodation process, I recommend you speak with an attorney familliar with ADA as it is handled in your circuit. That may end up being more expensive than accomodating her, depending on what accomodations are possible.