> without infinite cells?

To consider any system Turing complete you have to extend it to having infinite memory. This is why all actual, non-theoretical computers are equivalent to finite state machines (or linear bounded automata [0]).

[0] https://en.wikipedia.org/wiki/Linear_bounded_automaton

You can do looping by enabling iterative calculation mode, which has been supported in Excel for much longer than LAMBDA. In iterative mode, Excel attempts to resolve cyclic references in formulas by recalculating until the results converge, or a maximum number of iterations is reached. Unfortunately setting a maximum number of iterations is required... but one could argue that iterative mode does bring the spreadsheet model a bit closer to Turing completeness.