Advice to get owner to buy harness?

I have a client with a 5 year old lab, about 80 lbs. The dog is very sweet and smart but has bad habits both on and off leash, though he always sits when given the command. Off leash, it's jumping on people and paws on the counter/table, and crotch sniffing; on leash, he pulls really hard at least half of the walk. I walk him every weekday, and we've been practicing better manners to modest success. But last week he lunged, growled and tried to jump on an old lady who was passing us. Thankfully I had him short-leashed already and was able to control him before he touched her, but it definitely rattled me. I let the owner know right away in a very matter of fact way ("We had a mostly good walk but need to let you know about an incident...") but he never responded.

At the M&G 2 weeks ago, after we took his dog for a walk and he saw how much the dog pulled with me, the owner offered to buy a harness (I concurred and also suggested a halti). He has still not provided one, even after again telling me he would buy one last weekend. After the near-incident last week, I offered to purchase one and he could reimburse me, but he never replied to me.

So I'd like to know 1) how do I continue to ask the owner to follow through with getting harness without coming across as pushy (my last message was very direct about requesting the harness/halti) OR 2) should I just get one to use with his dog and bring it with me each time? Is that overstepping to do that? I sympathize with the owner - his job takes him away from home 12-14 hours a day - and I do like the dog. But I do not feel safe walking him as it stands with just a collar.