\documentclass{article}
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LuaTeX :

proposal 1: Lua\TeX

proposal 2: L\kern-0.1emu\kern-0.05ema\kern-0.12em\TeX

Proposal 3: L\kern-0.1em\raise0.1ex\hbox{u}\kern-0.05em\raise0.1ex\hbox{a}\kern-0.12em\TeX

LuaLaTeX :

proposal 1: Lua\LaTeX

proposal 2: L\kern-0.1emu\kern-0.05ema\kern-0.02em\LaTeX

Proposal 3: L\kern-0.1em\raise0.13ex\hbox{u}\kern-0.05em\raise0.13ex\hbox{a}\kern-0.1em\LaTeX

\newdimen\heightone
\newdimen\heighttwo
\setbox100=\hbox{L}
\heightone=\the\ht100
\heighttwo=\the\ht100
\setbox100=\hbox{u}
\advance\heightone by -\the\ht100
\setbox100=\hbox{a}
\advance\heighttwo by -\the\ht100
\divide\heighttwo by 3
Proposal 4: L\kern-0.17em\raise\heightone\hbox{u}\kern-0.05em\raise\heighttwo\hbox{a}\kern-0.12em\LaTeX

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