It is possible, but also extremely challenging and publishing takes more time, since you literally have to find the time. I myself have taken this path and I actually finance my own theoretical research from my profession as a medical practitioner. Software licenses and literature access are granted to me freely by having ties with a university department by remaining friends with a few of the staff, occassionally publishing together with them and helping them and their students with research, e.g. guiding students and advising w.r.t. methodology and technical aspects of research.
Also you should worry somewhat but again not worry too much about performance indicators such as having high citation indices; these indices do not necessarily measure what they are aiming to measure, namely how you and your work actually compare to your peers and their work. It is important to realize that such measures were invented for intended usage by administrators in order to systematically select, hire and pay researchers while giving the illusion of doing this in a scientific manner i.e. it is almost irrelevant for someone outside academia.
Moreover, in contrast to popular belief there are in fact many cases where different kinds of works and workers are actually incomparable, e.g. technical work focused on short term progress within a mature research programme as opposed to conceptual work focused on long term progress within a novel research programme, as well as the likes of Newton, Gauss or Grothendieck in comparison with their contemporaries: mathematical skill is not normally distributed!
Conceptual work is usually characteristic of the kind of original research that outsiders do, including Garrett Lisi and Julian Barbour, i.e. when one is not merely doing technical research but also doing foundational, conceptual and/or non-technical theoretical research. This kind of work usually tends to not be capable of being easily done by simply replacing oneself by someone else if that other person lacks the necessary idiosyncratic background, insight, creativity, vision and persistence required for this type of work; in such cases, citation indices are completely misleading metrics, practically of no use whatsoever a priori, perhaps only useful a posteriori.
From my own experience and academic circle, most recent graduates I have met in academia simply lack the creativity, drive and boldness to actually do real foundational work while the majority of graduate students are simply incapable of entirely creating and running their own original research programme at a sophisticated level; instead, they opt for lower hanging fruit and a safer career path. Only a few of them become capable of doing this somewhat later in life and even then they tend - due to their training - to be more proficient at being a specialist, while what is required for such work is the mind of a generalist.
Historically, there are loads of big names to be named for which the above characterization was true, and it is usually more true for theoreticians and mathematicians who do more creative mathematical work constructing new foundations both in physics and in mathematics; think of the likes of Newton, Euler, Gauss, Riemann, Lagrange, Hamilton, Ramanujan, Einstein, Poincaré, Feynman and so on who tended to be guided more for deeply personal reasons than by what academia and the contemporary literature wanted. Notice how the founders of QT are not on this list; this has a lot to do with the current foundations of QT still being an embarrassment and I maintain that completing the research programme of constructive QFT is the only way out for QT, but I digress.
As I have mentioned, foundational work actually requires creativity, but creativity while necessary is not sufficient. One has to also be trained in doing academic research, i.e. know how to effectively read the literature, find reviews, critical appraisal of topics, mastery of certain techniques, familiarity with certain theories and so on; this skillset is most effectively learned by staying within academia, but again that is not necessary especially if one has a mentor, close friend or family member who is in academia and can guide them through such hoops.
In any case, with sufficient discipline this can be self-taught as well but it is a lot of work and there aren't (m)any guides available i.e. you have to pick yourself up by your own bootstraps and (re)invent this for yourself; this is why these skills are best picked up by shadowing, emulation and osmosis of the day to day activities of active researchers.
