If it comes to why you are leaving your current job, depending upon why you actually left you could be able to give honest answers, half truths than hide the major reason, and twist the facts enough that it would be best described as a lie.
When asked what you are looking for in a new company, rarely will it be perceived positive to give any importance to money at that stage of the interview. Benefits can be mentioned, but you will have a better interview if you can give an answer closer aligned to the business you are interviewing at.
A major one is when you are asked what your current salary is, lying can be more beneficial than either not answering or telling the truth. You can stretch the truth a bit, say "A little under $130,000" when it is actually "101,000 plus a bonus that the company didn't give out last year". Is 101 a little under 130? It is subjective, and in some cases that wouldn't be a lie, but in this case it definitely stretches the truth.
Now, I'm not advocating lying about stuff on the technical side. Well, not by much. If someone in HR is asking if you have 15+ years experience in Rust (to those not familiar, it has only been about about 10 years), responding with an affirmative style answer is probably reasonable if you are experienced in the language. Don't do something like saying "Yes". More "I am very experienced in Rust and have had 3 large scale Rust products deployed with numerous smaller ones." This ends up being much better than trying to correct the HR rep that the language hasn't been out long enough for someone to have 15 years experience and better than answering no.
Examples of what I mean by deflection:
"My greatest weakness is for Gouda cheese."
"If I knew what my weaknesses were I would already have worked to resolve them."
"Triceps."
"I don't have any weakness, what are you talking about?"
"My biggest weakness is probably job interviews, compared to anything else I do my interviewing skills are really bad..."
More realistically: honestly explaining that some of my greatest strengths are weaknesses in other settings.
For example, talking about being somewhat OCD about things can be considered a weakness. But for some jobs in this field, a little OCD is not necessarily a bad thing.
If they asked what is one of your weaknesses and how are you working to overcome it, then that is a perfectly legitimate answer. Perhaps too many interviewers ask for the biggest weakness when they actually mean to ask a question more like that.
Of course everyone who asks this question is looking for how you reply, and don't necessarily believe you'll tell them the absolute truth.
For example: many companies insist on asking how you did "x" (for example solves a conflict of idea of solution) in situation "y" (for example between two teams in same department) and you are obliged to answer something, even if you never been in that situation (a certain multinational company for example asked me that question three times across two different attempts to join them, both of times I failed because this question, I never worked in a company with many departments).
After a lot of Glassdoor reading found out people that got the jobs I wanted, all lied outright, not just embellishments, but outright inventing things that sound plausible.
That some people manage to escape the requirement by lying doesn't mean lying is the intended strategy.
If your experience is only in companies with a handful engineers, yes, it can unfortunately be pretty hard to get a senior position at larger companies. It's not impossible, but people will have justified worries about whether you can handle the responsibilities.
In large corporations technical responsibility is often more distributed than in startups just due to size, so your technical skills, while important, are typically less important than they would be in small-business/startup land. What fills in the gap is communication skills and your ability to navigate corporate social networks. If you can't conflict resolve issues between engineering teams, well guess what? That engineering team you can't work with is going to hold you up and cost the company money while your superior, who really has better things to do, has to take time out of their day to address the issue you should have been able to handle.
Not saying it should be a mandatory skill, but you can't blame large corporations for filtering for it. It's a factor.
Now, working in a large multinational company would help ensure you have that kind of experience, but that's not your only option.
And how difficult do you think it is to learn this skill?
If it's an everyday occurrence in huge companies, and any new hires above entry level are expected to know how to do it, it sounds like something anyone and everyone will learn. Which sounds like a real easy skill.
If it's a real easy skill, why do you need to have it already when you join? Why can't you learn it on the job, like you learn a bazillion other skills?
This kind of thing comes up a lot with technical stuff... people think that X (something you can look up on wikipedia or SO and teach yourself in an hour or two tops) is really important, therefore they can't hire anyone who hasn't learned X. But whoever they hire must be a person who's super eager to learn new stuff.
So you don't want to give people the level of independent responsibility a senior title carries unless they've already learned how to avoid that.
Many times, when they ask a specific question, they're not hard-locked on getting an exact answer that is 100% directly related to that exact situation. They're also looking to see how you might slightly redirect the question to something that is relevant to your experience, and then how you answer that.
Of course, sometimes they are hard-locked onto an exact answer to that precise situation, and if you don't have that experience, then you're done. You're not likely to know in advance if that's the case, but at least you got more interviewing experience, and you learned of another place that you do not want to work.