So my security gate will not recognize my motorcycle when I exit my apartment building. I have to stop, get off of my bike, walk all the way around, enter the code, and walk back to my bike. Then I’m able to go about my day. I’m asking if I can sue for lost wages because it’s taking time out of my day. I’m losing work because I’m an independent contractor. I talked to management multiple times and they still have not done anything about it. It’s been going on for two months
I’m asking if I can sue for lost wages because it’s taking time out of my day
No, that would be a frivolous claim. You did not specify how much time and effort the walk takes you on a daily basis, but it is extremely doubtful that you could viably claim lost wages. Suing the landlord for this would put you at high risk of being ordered to pay his attorney fees, which surely will exceed that fictitious loss.
The allegation "I'm losing work because I’m an independent contractor" is untenable and makes no sense. By that token, a full-time employee typically is more constrained (for instance, in terms of schedule) than an independent contractor. It is also questionable that the time you spend walking back and forth when leaving your apartment is comparable to the time it takes you to do your job or get more clients. Depending on your location, the landlord would defeat your claim also on grounds that you could --and unjustifiably decline to-- take the bus or seek other arrangements if the issue truly were causing you provable losses.
It is also very unlikely that the continued failure to recognize your motorcycle would support a claim of breach of contract, since the terms of a lease hardly ever address that kind of minor details.
The only circumstance whereby you would have a viable claim is if you were handicapped, but your description nowhere reflects that that is the case. Even in that scenario, the nature of your claim would be other than "lost wages" and mostly would warrant injunctive relief.