Time-wise, there is no benefit to having a disability lawyer. Your claim isn't going to take precedence over anyone else's claim because you have a lawyer. One thing that I can say for certain though, is that if you have a good lawyer with knowledge of the SSDI process, the likelihood of winning and not having to appeal becomes greater for as long as evidence exists for you to rate it.
SSA follows the Blue Book for disability evaluation while VA follows 38 CFR. It takes time, and by time, I mean days to months to learn about your conditions to rate the proper disability rating from both agencies following different rulebooks.
I did my SSDI on my own over about 15 years and 2 appeals, but I kept all my retroactive pay. It was just something new to learn and argue in court vs. their vocational expert (and I think medical expert testimony, but they weren't present). It was hard for me to get points across being an introvert riddled with anxiety, but the vocational expert couldn't find me suitable, even with an educational background. If I had a lawyer, you better bet that the time of getting my SSDI award would've been quicker, but I would have also had to pay something like 30% of my retroactive backpay, which in hindsight wouldn't have been that much because the award would've been within months and not over a decade.
It's hard for me to trust anyone, let alone lawyers. So, I learned the Blue Book that was pertinent to my claim. It took appeals, but I got a partially favorable decision that resulted in about $20,000 less in retroactive backpay because I was late to one appeal as I thought it was over by then, until learning that it wasn't over, and I kept fighting. It still worked out in my favor with a lot in retroactive backpay after my battle with the Social Security Administration that helped pay for my home, so I really can't complain there. It would have been nice to have a monthly paycheck from the beginning to not pinch pennies, but I don't think I would be a homeowner without the retroactive award because it would have been hard to save.
Good luck with your claim!