You can execute below script against the SQL Server instance and check whether LiteSpeed is installed on the server or not.

T-SQL script is checking registry to check the LiteSpeed version value.

declare @regkeyval varchar(20), @value varchar(255), @rc int
exec @rc=master.dbo.xp_regread 
  @rootkey= 'hkey_local_machine',
  @key='software\imceda\sqllitespeed\engine',
  @value_name='version',
  @regkeyval=@value output

set @value =isnull(@value,'-') 

if @value <> '-'
select 
 @@servername as SQLInstanceName
,case serverproperty('IsClustered') when 1 then cast(serverproperty('computernamephysicalnetbios') as varchar)
 else cast(serverproperty('machinename') as varchar)
 end as WindowsServerName
,@value as LiteSpeedVersion 
,'LiteSpeed is installed' as LiteSpeedStautsCheck
else
select 
 @@servername as SQLInstanceName
,case serverproperty('IsClustered') when 1 then cast(serverproperty('computernamephysicalnetbios') as varchar)
 else cast(serverproperty('machinename') as varchar)
 end as WindowsServerName
,'LiteSpeed is not installed' as LiteSpeedStautsCheck