The easiest way to handle this would be to bring your own lock. Depending on the cabinet's configuration that might not be practical.

Anyway... you asked:

I keep prescription medication in my drawers. Does this affect my case?

This makes your case 'open and shut' in my opinion.

Is it OK to ask for a lock to be put on the drawers? How can I approach the matter?

"I have prescription medications that need to be secured in my cabinet.
How can I get a lock for it? It can't be a shared key."

Asking for no reason whatsoever might raise some questions.
Asking to lock up medications is completely different... it is always acceptable.

The easiest way to handle this would be to bring your own lock. Depending on the cabinet's configuration that might not be practical.

Anyway... You asked:

I keep prescription medication in my drawers. Does this affect my case?

This makes your case 'open and shut' in my opinion.

Is it OK to ask for a lock to be put on the drawers? How can I approach the matter?

"I have prescription medications that need to be secured in my cabinet.
How can I get a lock for it? It can't be a shared key."

Asking for no reason whatsoever might raise some questions.
Asking to lock up medications is completely different... it is always acceptable.

The easiest way to handle this would be to bring your own lock. Depending on the cabinet's configuration that might not be practical.

Anyway... you asked:

I keep prescription medication in my drawers. Does this affect my case?

This makes your case open/closed in my opinion.

Is it OK to ask for a lock to be put on the drawers? How can I approach the matter?

"I have prescription medications that need to be secured in my cabinet.
How can I get a lock for it? It can't be a shared key."

Asking for no reason whatsoever might raise some questions.
Asking to lock up medications is completely different... it is always acceptable.

The easiest way to handle this would be to bring your own lock. Depending on the cabinet's configuration that might not be practical.

Anyway... you asked:

I keep prescription medication in my drawers. Does this affect my case?

This makes your case 'open and shut' in my opinion.

Is it OK to ask for a lock to be put on the drawers? How can I approach the matter?

"I have prescription medications that need to be secured in my cabinet.
How can I get a lock for it? It can't be a shared key."

Asking for no reason whatsoever might raise some questions.
Asking to lock up medications is completely different... it is always acceptable.