  Mart{\'\i}nez-Pe{\~n}as and Kschischang (IEEE Trans.\ Inf.\ Theory, 2019)
proposed lifted linearized Reed--Solomon codes as suitable codes for error
control in multishot network coding. We show how to construct and decode
\ac{LILRS} codes. Compared to the construction by
Mart{\'\i}nez-Pe{\~n}as--Kschischang, interleaving allows to increase the
decoding region significantly and decreases the overhead due to the lifting
(i.e., increases the code rate), at the cost of an increased packet size. We
propose two decoding schemes for \ac{LILRS} that are both capable of correcting
insertions and deletions beyond half the minimum distance of the code by either
allowing a list or a small decoding failure probability. We propose a
probabilistic unique {\LOlike} decoder for \ac{LILRS} codes and an efficient
interpolation-based decoding scheme that can be either used as a list decoder
(with exponential worst-case list size) or as a probabilistic unique decoder.
We derive upper bounds on the decoding failure probability of the
probabilistic-unique decoders which show that the decoding failure probability
is very small for most channel realizations up to the maximal decoding radius.
The tightness of the bounds is verified by Monte Carlo simulations.
