Depends on the person, but real friends - yes, I would lend money without question.
I have borrowed money from one friend a few times and it has never affected our friendship, but she is very financially comfortable so she doesn't 'need' the money she lends me. In fact, I owe her £500 right now and when I asked her for the details to make the transfer, she said don't worry if you're short, don't put yourself out to pay me back right away. To be honest, if I never paid her back she wouldn't bat an eyelid but of course I will.
When we were teens/early twenties, I had plenty of money and she was on a tight budget, so the roles have reversed. Back then, I covered stuff from time to time without keeping a tab and never expected anything back. Not the same as a loan, but the sentiment was the same - we have each other's backs.
Lending to people who might fritter it away or never pay you back, or lending large sums (which is relative, of course, to your circumstances) is a different matter.
In your situation, OP, I can't imagine what the issue is. Are you perhaps overthinking it? If you really feel tension there then I'm not sure what to advise, as you did everything right. She didn't need to lend you the money if she wasn't comfortable with it.