Most of the times, I don't lol. Yes, there's no loudness in my laugh at all. And, 'lol' is probably used by everyone on the Internet/mobile even though when they laugh little. 'lol' is also used when the matter is not of some joke [However, I strictly avoid such usage].

For instance, in chat...

I know you are at Ruby's house
lol, I've not visited hers for past one month.

Now, if I use 'haha', is it considered offensive? Especially to native speakers. Let's say, I'm talking to my client who is from London or NYC. If she says something little funny which should not be replied with LOUD laughing, is it okay to use 'hahaha'. Will she consider that as an offensive gesture?

For instance...

Julia: Hello Maulik, I was busy yesterday. Sorry, I could not contact you.
Me: That is fine.
Julia: Yeah...I was pissed off; my boss flooded my inbox with loads of work.
Me: lol/hahaha/haha I hope you are okay now!

Finally, does the number of repetition matter? "Haha" is okay but not 'Hahaha' which may have a bit of offensiveness?

Is it okay if I use 'lol' there? I don't think so...it's not something I'll laugh out loud.

I'd like to clear that in this example, Julia is NOT my bosom-friend. She's a client and we know each other for past 10 days. That's it.