All three remain well adrift of the leading Test performers of the past six years, Lyon's fellow spinners Rangana Herath from Sri Lanka (305 wickets from 56 matches) and Ravi Ashwin from India who has snared 292 from 52 Tests with his off-spin.
Tamim was the slower of the two, especially in the first session, but even then he attacked Lyon - the main threat as the first-choice off-spinner on a spinning wicket.
In 2008, Australia were scheduled to host Bangladesh for two winter Tests, but that series was postponed until 2010 due to a clash with the Beijing Olympics. "Whatever the strengths they have, Australia are always tough opposition", he added. It would be a truly remarkable achievement, coming from a country that plays relatively little Test cricket.
The hosts are hoping Shakib, off-spinner Mehedi Hasan and left-arm spinner Taijul Islam can undo Australia's formidable batting line-up.
All-rounder Ashton Agar returned to Australian Test team after four years while the visitors also drafted in batsman Usman Khawaja.
Earlier, the Tigers were all out for 260 despite fifties from Tamim Iqbal and Shakib Al Hasan, as the other batsmen were subdued by a controlled Australian bowling.
Jose Mourinho: United have moved up a level
MUTV's Paddy Crerand: "Another terrific display by United and it's great to see the defence conceding no goals again". Martial's inclusion has come as bad news for Marcus Rashford , who drops to the substitutes' bench.
If he looked only mildly pleased at the milestone, it said more for a day of hard work and perseverance than anything else.
Full pitch: Bangladesh's Tamim Iqbal at the crease on day one of the first test in Dhaka. "They batted with goal and chose their bowlers very precisely unlike before when we were not sure what we really wanted to achieve".
Dhaka: Nathan Lyon said Friday he was not carried away by the prospect of overtaking legendary Richie Benaud to become Australia's second most successful spinner during the forthcoming two-Test series against Bangladesh.
"I think for us Australians will be about bowling in partnerships and bowling well together to take 20 wickets", said Lyon. "I won't say in all conditions, but in our conditions, we are better than them", said Shakib.
Australia: Steve Smith (captain), David Warner, Ashton Agar, Hilton Cartwright, Pat Cummins, Peter Handscomb, Matthew Wade, Josh Hazlewood, Usman Khawaja, Nathan Lyon, Glenn Maxwell, Matt Renshaw, Mitchell Swepson and Jackson Bird.
"I think the two guys batted very fearless", Lyon said.
The Aussies are looking for their first series victory on the sub-continent since beating Sri Lanka 1-0 in 2011. "We need to do well in all aspects if we want to win the Tests".