Lillee, if transported as a 16 year old into the year 2006 or something, would have access to different training, nutrition, better video analysis, etc, and he would have to adapt his game to these new things. Maybe he would, or maybe he woul be put off by some of the differences, we don't know.
However, with all that said, the approach to bowling fast that he had would be virtually the same as from his time. And with all the potential improvements mentioned the end result might be 3-5 kph faster speed, i.e. virtually the same (that too only if he felt it best suited to his new game, his pace from that time is perfectly within range for so called fast-medium bowlers now, as is).
That is far from what can be said for Barnes, whose very style of bowling is extinct in modern cricket (and with good reason). The history of cricket includes a spectrum of techniques, and saw a big transformation, especially in the early half of the 20th century, but the optimization of the professional Era somewhat locked into place the range of skillsets and techniques we see on a cricket pitch. No one is held back anymore, and the only major changes have been safety equipment, and an increase in batting aggression. These are not aspects which professional Era players would not be able to adapt to, on the whole. (I will caveat that I do think the overall quality and skill displayed at the highest level of cricket is always improving incrementally, that's why you'd have to time travel a player in a development stage, rather than as they were in career, to make it fair as I do believe the older player would be generally disadvantaged in skill.)