The midfielder completed a move to the Chinese Super League this week after being linked with the Reds.
The Reds made a big money offer for the Shakhtar Donetsk star late on in the January transfer window but were eventually unable to agree a fee for the player.
He has since moved to the Chinese Super League, with Jiangsu Suning paying a Chinese transfer record of £38.4million to secure his services this week.
That naturally left Liverpool fans feeling disappointed they had missed out on the player but Lawrenson says it may have been a lucky escape for Jurgen Klopp’s side.
"Klopp was only keen on bringing somebody in if they would improve the current squad and clearly there wasn't anybody available," he told the Liverpool Echo.
"There was in Shakhtar Donetsk forward Alex Teixeira. However, the Ukrainian side priced the player out of Liverpool's range and instead he's ended up going to China. That he's gone there tells you everything.
"He could have waited until June and moved to the Premier League, but clearly all that stuff about wanting to play in England wasn't true. In that respect, we may have dodged a bullet."
While they may have accepted the lack of players arriving in the January transfer window, the Reds fan base will surely expect a big overhaul in the summer.
There are several areas of the team that need strengthening, with Liverpoool's defence likely to be chief among Klopp's thoughts and - many supporters will hope - a new goalkeeper after Simon Mignolet’s latest error against Sunderland.
A new striker may also be in order, with Christian Benteke continuing to struggle and Daniel Sturridge’s long-term fitness still a chief point of concern.