My conjecture is as follows:
Take any number. It will become a palindrome eventually through the same reversal process used for Lychrel numbers except if the term (first term is excluded) starts with 1, the 1 is disregarded.
For example: 196+691=887
887+788=1675 => 675
675+576=1251 => 251
251+152=403
403+304=707 is a palindrome.
Can anyone prove this or find a counterexample? Thanks for your time and help!
The smallest counter-example is $10039547$, which gets into a cycle:
$$ \begin{array}{} \color{red}{84632548} \\ 69156196 \\ 38321392 \\ 67633775 \\ 25367451 \\ 40843803 \\ 71678607 \\ 42366224 \\ \color{red}{84632548} \\ \end{array} $$ Found by exhaustive brute-force search.